Shape and space · Ages 11–12
Angles worksheet
Covers: The protractor and naming angles, Angles on a straight line and around a point, Vertically opposite angles and angles at a point, Angles in triangles and quadrilaterals, Angles of regular polygons
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Angles worksheet
Shape and space · Ages 11–12
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A protractor measures the angle. How many degrees is ∠AOB?
Answer:
2.A protractor measures the angle. How many degrees is ∠AOB?
Answer:
3.∠x = ?°
Answer:
4.∠x = ?°
Answer:
5.∠x = ?°
Answer:
6.Three straight lines cross at one point. What is the angle marked ? in degrees?
Answer:
7.Quadrilateral: ∠x = ?°
Answer:
8.Right-angled triangle: ∠x = ?°
Answer:
9.What do the angles of a regular polygon with 5 sides add up to, in degrees?
Answer:
10.The picture shows a regular polygon. What is the angle marked ? in degrees?
Answer:
Part B: Choose, or true or false (2 marks each)
11.Which angle is marked in the picture?
- A. ∠BCD
- B. ∠ABC
- C. ∠DAB
- D. ∠CDA
Choose the right answer
Answer:
12.Two straight lines cross. In the picture, x = 140°.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A door is opened 40° from shut, then 35° more. How many more degrees must it open to make a straight angle with where it started?
Working:
Answer:
14.A clock's minute hand points at 12 and its hour hand at 1. How many degrees is the smaller angle between the hands?
Working:
Answer:
15.A right angle is split into two angles by a straight line. One of them is 37°. How many degrees is the other?
Working:
Answer:
16.Chi-keung cuts a pizza from its centre into three slices. Two are the same size, and the third slice's tip is 180°. How many degrees is the tip of each of the equal slices?
Working:
Answer:
17.Two angles of a triangle are 60° and 94°. How many degrees is the third angle?
Working:
Answer:
18.Three tiles meet at a point with no gap. One is a regular polygon with 6 sides and one has 5 sides. How many degrees is the third tile's angle at that point?
Working:
Answer:
Show the answers and working
Angles worksheet: Answers and working
Part A: Working out and filling in
1. 70°
Which side's 0° is OA on? Read from that scale's 0° and see where OB points.
OA is on the 0° at the right, so read the inner scale: OB points at 70, ∠AOB = 70°.
2. 80°
OA is on the 0° at the left. Is that the inner or outer scale? Read that same scale.
OA is on the 0° at the left, so read the outer scale: OB points at 80, ∠AOB = 80° (the inner 100 belongs to the other angle).
3. ∠x = 20°
A right angle is 90°: 90 − 70 = 20, so x = 20°
4. ∠x = 58°
Angles on a straight line make 180°: 180 − 122 = 58, so x = 58°
5. ∠x = 54°
Angles on a straight line make 180°: 180 − 126 = 54, so x = 54°
6. 40°
Find the angle opposite 80° first. Does it lie on one straight line with 60° and ?
The angle opposite 80° is also 80°, and it lies on one line with 60° and ?: 180 − 60 − 80 = 40.
7. Quadrilateral: ∠x = 55°
A quadrilateral's four angles make 360°: add the angles you know first, 80 + 117 = 197, 197 + 108 = 305, 360 − 305 = 55, so x = 55°
8. Right-angled triangle: ∠x = 25°
A triangle's three angles make 180°, one of them a right angle, 90°: 90 + 65 = 155, 180 − 155 = 25, so x = 25°
9. 540°
Drawing diagonals from one corner, how many triangles does a shape with 5 sides split into? Each triangle is 180°.
It splits into 5 − 2 = 3 triangles: 3 × 180 = 540.
10. 135°
Count the sides first, then find the angle sum with (sides − 2) × 180°.
Count the sides: 8. The angles add to (8 − 2) × 180 = 1080, each 1080 ÷ 8 = 135.
Part B: Choose, or true or false
11. D. ∠CDA
First see which corner the marked angle is at; that letter goes in the middle of the name.
The middle letter of an angle's name is its corner: see which corner is marked.
12. False
Look where x is compared with 140°: opposite it, or beside it?
x equals 140° only if they are opposite; if they are side by side, x = 180 − 140. Here x = 40°.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 105°
A straight angle is 180°. First find how far it has opened: 40 + 35.
A straight angle is 180°: 40 + 35 = 75° so far, 180 − 75 = 105°.
14. 30°
A clock face's 360° is split into 12 equal gaps. The minute hand is on 12 and the hour hand on 1: how many gaps apart?
Neighbouring numbers on a clock are 360° ÷ 12 = 30° apart; the gaps between the hands × 30°, the smaller way round: 30°.
15. A right angle is split into two angles by a straight line. One of them is 37°. How many degrees is the other? (Answer: 53 degrees)
90 − 37 = 53
16. 90°
Round the centre is 360°. Subtract the third slice's 180° first; the other two share the rest.
Round the centre is 360°: 360 − 180 = 180, shared by two: 180 ÷ 2 = 90.
17. Two angles of a triangle are 60° and 94°. How many degrees is the third angle? (Answer: 26 degrees)
180 − 60 − 94 = 26
18. 132°
Find each angle of the 6-sided and 5-sided tiles first; round a point is 360°.
The 6-sided one's angle is 120° and the 5-sided one's 108°; round a point is 360°: 360 − 120 − 108 = 132.
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