Shape and space · Ages 11–12

Vertically opposite angles and angles at a point worksheet

Part of: Angles

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Shape and space · Ages 11–12

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.Two straight lines cross. What is the angle marked ? in degrees?
Answer:
2.Two straight lines cross. What is the angle marked ? in degrees?
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3.The angles in the picture are all round one point, and the two x's are equal. How many degrees is x?
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4.Two straight lines cross. x = °, y = °, z = °
Fill in each blank
Answer:
5.Three straight lines cross at one point. What is the angle marked ? in degrees?
Answer:

13.Two straight roads cross at a junction, and one of the angles is 45°. How many degrees is the angle beside it?
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14.Ka-lok cuts a pizza from its centre into three slices. Two are the same size, and the third slice's tip is 190°. How many degrees is the tip of each of the equal slices?
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15.A pair of scissors crosses at the screw, and its blades open at 50°. How many degrees is the angle between the two handles on the other side?
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16.A windmill has 12 blades spread evenly round its centre. How many degrees is the angle between two blades next to each other?
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17.A round cake is cut from its centre into 4 pieces. Three of the pieces' tips are 110°, 45° and 80°. How many degrees is the fourth piece's tip?
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18.A round cake is cut from its centre into 4 pieces. Three of the pieces' tips are 90°, 110° and 110°. How many degrees is the fourth piece's tip?
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Show the answers and working

Vertically opposite angles and angles at a point worksheet: Answers and working

1. 145°
How is ? related to the angle given: opposite it, or beside it?
? and 145° are vertically opposite, and opposite angles are equal: ? = 145°.
2. 65°
? and 115° lie on one straight line. What do two angles side by side make?
? is beside 115° on one straight line: 180 − 115 = 65.
3. 55°
The angles round a point make 360°. Subtract 120° and 130° first to see what the two x's share.
Round a point is 360°: 360 − 120 − 130 = 110, shared by the two x's: 110 ÷ 2 = 55.
4. 105, 75, 105
x lies on a line with 75°. Which angles are y and z opposite?
x is on a line with 75°: 180 − 75 = 105; y is opposite 75°: 75; z is opposite x: 105.
5. 40°
Find the angle opposite 45° first. Does it lie on one straight line with 95° and ?
The angle opposite 45° is also 45°, and it lies on one line with 95° and ?: 180 − 95 − 45 = 40.

6. B. 160°
Opposite angles face each other where two lines cross. How do their sizes compare?
Vertically opposite angles are equal: 160°.
7. C. 140°
Opposite angles face each other where two lines cross. How do their sizes compare?
Vertically opposite angles are equal: 140°.
8. B. 145°
Opposite angles face each other where two lines cross. How do their sizes compare?
Vertically opposite angles are equal: 145°.
9. False
Look where x is compared with 130°: opposite it, or beside it?
x equals 130° only if they are opposite; if they are side by side, x = 180 − 130. Here x = 50°.
10. True
Look where x is compared with 55°: opposite it, or beside it?
x equals 55° only if they are opposite; if they are side by side, x = 180 − 55. Here x = 55°.
11. False
Look where x is compared with 145°: opposite it, or beside it?
x equals 145° only if they are opposite; if they are side by side, x = 180 − 145. Here x = 35°.
12. True
Look where x is compared with 35°: opposite it, or beside it?
x equals 35° only if they are opposite; if they are side by side, x = 180 − 35. Here x = 35°.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 135°
Two angles side by side lie on one straight line. What do they add up to?
Angles side by side are on one straight line: 180 − 45 = 135.
14. 85°
Round the centre is 360°. Subtract the third slice's 190° first; the other two share the rest.
Round the centre is 360°: 360 − 190 = 170, shared by two: 170 ÷ 2 = 85.
15. 50°
The blades and handles form two crossing straight lines. How is the blades' angle related to the handles'?
The two sides of the scissors are crossing straight lines, so the blades' angle and the handles' angle are opposite, and opposite angles are equal: 50°.
16. 30°
How many degrees are there round the centre? The 12 blades split it equally.
The angles round the centre make 360°: 360 ÷ 12 = 30.
17. 125°
Round the centre is 360°. Add the three tips, 110°, 45° and 80°, first.
Round the centre is 360°: 110 + 45 + 80 = 235, and 360 − 235 = 125.
18. 50°
Round the centre is 360°. Add the three tips, 90°, 110° and 110°, first.
Round the centre is 360°: 90 + 110 + 110 = 310, and 360 − 310 = 50.

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