Primary 4 Mathematics · Chapter 7 · Answers and explanations
Lesson 7.1: Recall: Acute, Right and Obtuse Angles (answers)
Section A · Multiple choice 4 marks
1. What kind of angle is shown?1 mark
(A) a right angle(B) an acute angle(C) an obtuse angle(D) a straight line
Answer: (B) an acute angleIt is smaller than a right angle (a square corner), so it is an acute angle.
2. What kind of angle is shown?1 mark
(A) an acute angle(B) a right angle(C) an obtuse angle(D) a straight line
Answer: (C) an obtuse angleIt is bigger than a right angle but smaller than a straight line, so it is an obtuse angle.
3. A right angle is the same as a turn of1 mark
(A) a half turn(B) three-quarters of a turn(C) a full turn(D) a quarter turn
Answer: (D) a quarter turnA full turn is 360°. A quarter turn is 360° ÷ 4 = 90°, which is a right angle.
4. Which angle is the biggest?1 mark
(A) Angle Y(B) Angle X(C) Angle Z(D) They are all the same
Answer: (A) Angle YAngle Y opens the widest, so it is the biggest. (X is 65°, Y is 140° and Z is 100°.)
Section B · Write your answer 11 marks
5. Is an angle of 150° acute, right or obtuse?1 mark
Answer: obtuseAn acute angle is less than 90° and a right angle is exactly 90°. 150° is more than 90° and less than 180°, so it is obtuse.
6. How many right angles make a half turn?1 mark
Answer: 2A half turn is 180°. 90° + 90° = 180°, so 2 right angles make a half turn.
7. How many right angles does a rectangle have?1 mark
Answer: 4All 4 corners of a rectangle are square corners (right angles).
8. The minute hand of a clock moves from 12 to 3. How many degrees does it turn?1 mark
Answer: 90°From 12 to 3 is a quarter turn, which is 90°.
9. Write the numbers of the obtuse angles.1 mark
Answer: Angles 3 and 4Angle 1 is smaller than a square corner (acute). Angle 2 is a square corner (right). Angles 3 and 4 are wider than a square corner but not a straight line, so they are obtuse.
10. Write acute, right or obtuse for each angle: X, Y and Z.2 marks
Answer: X: obtuse, Y: acute, Z: rightX is wider than a square corner (obtuse). Y is narrower than a square corner (acute). Z is exactly a square corner (right).
11. The minute hand of a clock moves from 12 to 3 and then from 3 to 6. How many degrees has it turned altogether? What turn is this?2 marks
Answer: 180°; a half turn12 to 3 is 90° and 3 to 6 is 90°. 90° + 90° = 180°, which is a half turn.
12. Write these angles in order, from the smallest to the biggest: 130°, 45°, 90°, 170°. Which of them are obtuse angles?2 marks
Answer: 45°, 90°, 130°, 170°; obtuse: 130° and 170°Order them: 45°, 90°, 130°, 170°. Obtuse angles are more than 90° and less than 180°, so 130° and 170° are obtuse. 45° is acute and 90° is a right angle.
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Primary 4 Mathematics · Chapter 7 · Answers and explanations
Lesson 7.2: Naming Angles (answers)
Section A · Multiple choice 4 marks
1. Which is the correct name of the marked angle?1 mark
(A) ∠BAC(B) ∠CAB(C) ∠ABC(D) ∠BCA
Answer: (C) ∠ABCThe vertex is B, where the two arms meet. The vertex letter goes in the middle, so the angle is ∠ABC.
2. In ∠PQR, which letter is the vertex?1 mark
(A) P(B) R(C) P and R(D) Q
Answer: (D) QThe vertex is the middle letter, so it is Q.
3. Which angle is marked in the triangle?1 mark
(A) ∠XZY(B) ∠ZXY(C) ∠XYZ(D) ∠YXZ
Answer: (A) ∠XZYThe marked angle is at Z, so Z is the middle letter. It is ∠XZY (or ∠YZX).
4. Which angle is the same as ∠DEF?1 mark
(A) ∠EDF(B) ∠FED(C) ∠DFE(D) ∠EFD
Answer: (B) ∠FED∠DEF and ∠FED both have E in the middle, so they are the same angle.
Section B · Write your answer 11 marks
5. Name the marked angle.1 mark
Answer: ∠MNK (or ∠KNM)The arms meet at N, so N goes in the middle: ∠MNK or ∠KNM.
6. The vertex of ∠STU is a point. Which letter names it?1 mark
Answer: TThe vertex is the middle letter, T.
7. Write another name for ∠ABC.1 mark
Answer: ∠CBASwap the first and last letters and keep the vertex B in the middle: ∠CBA.
8. ABCD is a rectangle. Name the marked angle.1 mark
Answer: ∠ADC (or ∠CDA)The marked angle is at corner D, so D goes in the middle: ∠ADC or ∠CDA.
9. True or false: ∠ABC and ∠ACB are the same angle.1 mark
Answer: False∠ABC has its vertex at B but ∠ACB has its vertex at C, so they are different angles.
10. Name the three angles of triangle PQR that are marked.2 marks
Answer: ∠QPR, ∠PQR, ∠PRQ (other orders of the outer letters are also correct)Write the vertex in the middle each time. At P: ∠QPR. At Q: ∠PQR. At R: ∠PRQ.
11. Name all the angles in the figure. Which one is the obtuse angle?2 marks
Answer: ∠AOB, ∠BOC, ∠AOC; ∠AOC is obtuseAll the angles have O as the vertex: ∠AOB, ∠BOC and ∠AOC. ∠AOC is the widest one and is more than a right angle, so it is obtuse.
12. Mei says the marked angle is ∠ABC. Raj says it is ∠BAC. Who is correct? Give a reason.2 marks
Answer: Mei is correctThe marked angle is at B, and the vertex letter must be in the middle. So it is ∠ABC. ∠BAC has its vertex at A.
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Primary 4 Mathematics · Chapter 7 · Answers and explanations
Lesson 7.3: Measuring Angles (answers)
Section A · Multiple choice 4 marks
1. What is the size of the angle?1 mark
(A) 140°(B) 50°(C) 130°(D) 40°
Answer: (D) 40°One arm is on 0 at the right, so read the outer scale that starts at 0 on the right. The other arm is at 40°.
2. What is the size of the angle?1 mark
(A) 65°(B) 115°(C) 55°(D) 125°
Answer: (A) 65°One arm is on 0 at the LEFT, so read the inner scale that starts at 0 on the left. The other arm is at 65°. (115° is the reading on the other scale.)
3. What is the size of the angle?1 mark
(A) 45°(B) 135°(C) 125°(D) 145°
Answer: (B) 135°The arm is on 0 at the right, so use the outer scale: 135°. The angle is wider than a square corner, so it is obtuse and 45° cannot be right.
4. When Sam measured an acute angle, he read 30° on one scale and 150° on the other scale. What is the size of the angle?1 mark
(A) 150°(B) 60°(C) 30°(D) 120°
Answer: (C) 30°An acute angle is less than 90°, so the size must be 30°.
Section B · Write your answer 11 marks
5. What is the size of the angle?1 mark
Answer: 70°Arm on 0 at the right, so read the outer scale. The other arm is at 70°.
6. What is the size of the angle?1 mark
Answer: 35°Arm on 0 at the left, so read the inner scale. The other arm is at 35°.
7. What is the size of the angle?1 mark
Answer: 115°Arm on 0 at the right, so read the outer scale: 115°. It is an obtuse angle.
8. What is the size of the angle?1 mark
Answer: 120°Arm on 0 at the left, so read the inner scale: 120°. It is an obtuse angle.
9. What is the size of the angle?1 mark
Answer: 85°Arm on 0 at the left, so read the inner scale: 85°. It is an acute angle.
10. Measure ∠XYZ. Is it acute, right or obtuse?2 marks
Answer: 150°; obtuseStart at 0 on the outer scale (the arm YX is on the right side). The other arm is at 150°. It is more than 90°, so it is obtuse.
11. Lina says ∠PQR is 110° because the arm is at 110 on the outer scale. Is she correct? What is the size of ∠PQR?2 marks
Answer: No; ∠PQR = 70°One arm is on 0 at the left, so Lina must use the inner scale, which gives 70°. The angle is acute (smaller than a square corner), so it cannot be 110°.
12. The two arms OB and OC are drawn from O. Find the size of ∠BOC.2 marks
Answer: 70°OB is at 35° and OC is at 105° on the outer scale. ∠BOC = 105° − 35° = 70°.
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Primary 4 Mathematics · Chapter 7 · Answers and explanations
Lesson 7.4: Drawing Angles (answers)
Section A · Multiple choice 4 marks
1. Mei wants to draw ∠ABC = 50°. Where should the centre of the protractor be placed?1 mark
(A) on B(B) on A(C) on C(D) on the middle of AB
Answer: (A) on BThe vertex is B (the middle letter). Put the centre of the protractor on the vertex B, with the baseline along arm BA.
2. Which is the best estimate of the size of this angle?1 mark
(A) 30°(B) 120°(C) 60°(D) 170°
Answer: (B) 120°It is wider than a square corner (90°) but not nearly a straight line (180°), so about 120° is the best estimate.
3. Sara wants to draw an angle of 130°. Her angle should be1 mark
(A) an acute angle(B) a right angle(C) an obtuse angle(D) a straight line
Answer: (C) an obtuse angle130° is more than 90° and less than 180°, so it is an obtuse angle.
4. Mei put the centre of the protractor on B and the baseline along BA. She made a dot at 55 on the inner scale (the red dot). She will join the dot to B. What angle will she draw?1 mark
(A) 125°(B) 35°(C) 65°(D) 55°
Answer: (D) 55°The arm BA is on 0 at the left, so Mei is using the inner scale. The dot is at 55, so ∠ABC = 55°. (125° is the number on the outer scale.)
Section B · Write your answer 11 marks
5. Using a ruler and a protractor, draw ∠ABC = 40°. The line BA is drawn for you.1 mark
Answer: Check: ray BC makes a 40° angle with BA (acute).Put the centre of the protractor on B and the baseline along BA. Start at 0 on the scale and count to 40. Make a dot, then join it to B with a ruler. Label the dot C.
6. Using a ruler and a protractor, draw ∠PQR = 75°. The line QP is drawn for you.1 mark
Answer: Check: ray QR makes a 75° angle with QP (acute).Put the centre on Q and the baseline along QP. Start at 0 and count to 75. Make a dot, join it to Q and label it R.
7. Using a ruler and a protractor, draw ∠XYZ = 120°. The line YX is drawn for you.1 mark
Answer: Check: ray YZ makes a 120° angle with YX (obtuse).Put the centre on Y and the baseline along YX. YX points to the left, so start at 0 on the inner scale and count to 120. Make a dot, join it to Y and label it Z.
8. Which angle is bigger, X or Y?1 mark
Answer: Angle YAngle Y opens wider than Angle X. Y is 100° and X is 35°.
9. Zara was asked to draw an angle of 80°. She drew the angle below. Is her angle correct? 1 mark
Answer: No; it is 100°One arm is on 0 at the left, so read the inner scale. The other arm is at 100, not 80. Zara used the wrong scale.
10. Using a ruler and a protractor, draw ∠XYZ = 145°. Is it acute, right or obtuse?2 marks
Answer: Check: 145° angle; obtusePut the centre on Y and the baseline along YX. Count to 145 from 0. Join the dot to Y. 145° is more than 90° and less than 180°, so it is an obtuse angle.
11. Tim was asked to draw an angle of 60°. He drew the angle below. Is it correct? How do you know?2 marks
Answer: No; it is 120° (obtuse), but 60° must be acute60° is smaller than a right angle, so it must be an acute angle. Tim's angle is wider than a square corner. He read the wrong scale (120° instead of 60°).
12. Draw ∠AOB = 30°. Then draw ∠BOC = 50° so that it is next to ∠AOB. What is the size of ∠AOC?2 marks
Answer: 80°Draw OB at 30° from OA. Then draw OC at 50° from OB, which is 30° + 50° = 80° from OA. ∠AOC = 80°.
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Primary 4 Mathematics · Chapter 7 · Answers and explanations
Chapter 7 Revision Paper: Angles (answers)
Section A · Multiple choice 10 marks
1. Which angle is an obtuse angle?1 mark
(A) Angle Y(B) Angle W(C) Angle X(D) Angle Z
Answer: (A) Angle YAn obtuse angle is wider than a square corner (90°) but smaller than a straight line. Angle Y is the only one wider than a square corner. Angle X is a right angle, and W and Z are acute.
2. Which statement is true?1 mark
(A) An obtuse angle is smaller than a right angle.(B) Two right angles make a straight line.(C) An acute angle is bigger than a right angle.(D) A right angle is 180°.
Answer: (B) Two right angles make a straight line.A right angle is 90°, so two right angles make 90° + 90° = 180°, a straight line. An obtuse angle is bigger than 90° and an acute angle is smaller than 90°.
3. The minute hand of a clock moves from 12 to 9 (clockwise). What angle does it turn through?1 mark
(A) 90°(B) 180°(C) 270°(D) 360°
Answer: (C) 270°12 to 3 is 90°, 3 to 6 is another 90° and 6 to 9 is another 90°. 90° + 90° + 90° = 270°. This is a three-quarter turn.
4. Which is the correct name of the marked angle?1 mark
(A) ∠EDF(B) ∠DFE(C) ∠FDE(D) ∠DEF
Answer: (D) ∠DEFThe marked angle is at corner E, so E is the vertex. The vertex letter goes in the middle: ∠DEF (or ∠FED).
5. In the figure, ∠AOB = 40° and ∠BOC = 50°. Which angle is a right angle?1 mark
(A) ∠AOC(B) ∠AOB(C) ∠BOC(D) ∠ABC
Answer: (A) ∠AOC∠AOC = ∠AOB + ∠BOC = 40° + 50° = 90°, so ∠AOC is a right angle. ∠ABC has its vertex at B, so it is a different angle.
6. What is the size of the angle?1 mark
(A) 55°(B) 125°(C) 135°(D) 115°
Answer: (B) 125°One arm is on 0 at the right, so read the outer scale. The other arm is at 125°. The angle is wider than a square corner, so 55° cannot be right.
7. Dev measured an obtuse angle. He read 70° on one scale and 110° on the other scale. What is the size of the angle?1 mark
(A) 70°(B) 180°(C) 110°(D) 40°
Answer: (C) 110°An obtuse angle is more than 90°, so the size must be 110°. 70° is the reading on the other scale.
8. Ria wants to draw ∠XYZ = 65°. The arm YX points to the right, on 0 of the baseline. Which scale should she use?1 mark
(A) the inner scale, which starts at 0 on the left(B) the scale that gives the bigger number(C) it does not matter which scale she uses(D) the outer scale, which starts at 0 on the right
Answer: (D) the outer scale, which starts at 0 on the rightAlways start counting from the 0 that is on the arm. The arm YX is on the 0 at the right, so use the scale that starts at 0 on the right (the outer scale).
9. What is the best estimate of the size of this angle?1 mark
(A) 135°(B) 45°(C) 90°(D) 170°
Answer: (A) 135°It is clearly wider than a square corner (90°), but it is not nearly a straight line (180°). So 135° is the best estimate.
10. Rina is drawing ∠ABC. The arm BA is on 0 at the left. She puts a dot at the red dot and will join it to B. What size of angle will she draw?1 mark
(A) 135°(B) 45°(C) 55°(D) 35°
Answer: (B) 45°The arm BA is on 0 at the left, so use the inner scale. The red dot is at 45 on the inner scale, so the angle is 45°. (135° is the number on the outer scale.)
Section B · Short answers 4 marks
11. How many right angles make a three-quarter turn?1 mark
Answer: 3One right angle is a quarter turn. A three-quarter turn is 3 quarter turns, so it is 3 right angles (270°).
12. Name the marked angle.1 mark
Answer: ∠XYZ (or ∠ZYX)The arms meet at Y, so Y is the vertex and goes in the middle: ∠XYZ or ∠ZYX.
13. What is the size of ∠XYZ?1 mark
Answer: 110°The arm YX is on 0 at the left, so read the inner scale. The other arm is at 110°. It is an obtuse angle.
14. Using a ruler and a protractor, draw ∠KLM = 125°. The line LK is drawn for you.1 mark
Answer: Check: ray LM makes a 125° angle with LK (obtuse).Put the centre of the protractor on L and the baseline along LK. LK points to the left, so start at 0 on the inner scale and count to 125. Make a dot, join it to L with a ruler and label it M.
Section C · Show your working 16 marks
15. A door is opened through an angle of 65°. It is then opened a further 40°. (a) What is the angle now? (b) Is the angle acute, right or obtuse?2 marks
Answer: (a) 105° (b) obtuse(a) 65° + 40° = 105°. (b) 105° is more than 90° and less than 180°, so it is an obtuse angle.
16. (a) Name the three marked angles in triangle FGH. (b) Which of them is the obtuse angle?2 marks
Answer: (a) ∠GFH, ∠FGH, ∠FHG (b) ∠FHG(a) Put the vertex letter in the middle each time: at F it is ∠GFH, at G it is ∠FGH and at H it is ∠FHG. (b) The angle at H opens wider than a square corner, so ∠FHG is obtuse.
17. OA lies along the baseline of the protractor. Find ∠BOC. Is it acute, right or obtuse?2 marks
Answer: 65°; acuteOA is on 0 at the left, so read the inner scale. OB is at 40° and OC is at 105°. ∠BOC = 105° − 40° = 65°. It is less than 90°, so it is acute.
18. Ria says ∠XYZ is 105° because the arm is at 105 on the inner scale. Is she correct? What is the size of ∠XYZ?2 marks
Answer: No; ∠XYZ = 75°The arm YX is on 0 at the right, so Ria must use the outer scale, which gives 75°. The angle is smaller than a square corner, so it is acute and cannot be 105°.
19. Draw ∠AOB = 45°. Then draw ∠BOC = 65° next to it, so that OB is between OA and OC. What is the size of ∠AOC? Is it acute, right or obtuse?2 marks
Answer: ∠AOC = 110°; obtuseDraw OB at 45° from OA. Then draw OC at 65° from OB, which is 45° + 65° = 110° from OA. 110° is more than 90°, so ∠AOC is obtuse.
20. (a) Name the angle shown in the figure, using the letters E, F and G. (b) What is its size?2 marks
Answer: (a) ∠EFG (or ∠GFE) (b) 155°(a) The arms meet at F, so F goes in the middle: ∠EFG. (b) Arm FE is on 0 at the left, so read the inner scale: 155°. It is obtuse.
21. In the figure, ∠AOB = 25°. ∠BOC is 3 times as big as ∠AOB. ∠COD = 20°. (a) Find ∠AOC. (b) Find ∠AOD. Is it acute, right or obtuse?2 marks
Answer: (a) 100° (b) 120°; obtuse∠BOC = 3 × 25° = 75°. (a) ∠AOC = 25° + 75° = 100°. (b) ∠AOD = 100° + 20° = 120°. It is more than 90°, so it is obtuse.
22. ∠AOD is a right angle. ∠AOB = 25°. ∠BOC is 20° bigger than ∠AOB. (a) Find ∠COD. (b) Find ∠BOD.2 marks