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