Angles on a straight line and around a point worksheet

Part A: Working out and filling in

1. 1. ∠x = 180°

   Angles round a point make 360°: add the angles you know first, 75 + 105 = 180, 360 − 180 = 180, so x = 180°

2. 2. ∠x = 35°

   Angles on a straight line make 180°: 180 − 145 = 35, so x = 35°

3. 3. ∠x = 159°

   Angles round a point make 360°: add the angles you know first, 146 + 55 = 201, 360 − 201 = 159, so x = 159°

4. 4. ∠x = 125°

   Angles on a straight line make 180°: 180 − 55 = 125, so x = 125°

5. 5. ∠x = 180°

   Angles round a point make 360°: add the angles you know first, 90 + 90 = 180, 360 − 180 = 180, so x = 180°

6. 6. ∠x = 205°

   Angles round a point make 360°: add the angles you know first, 95 + 60 = 155, 360 − 155 = 205, so x = 205°

7. 7. ∠x = 30°

   A right angle is 90°: 90 − 60 = 30, so x = 30°

8. 8. ∠x = 148°

   Angles round a point make 360°: add the angles you know first, 120 + 92 = 212, 360 − 212 = 148, so x = 148°

9. 9. ∠x = 71°

   A right angle is 90°: 90 − 19 = 71, so x = 71°

10. 10. ∠x = 140°

    Angles round a point make 360°: add the angles you know first, 150 + 70 = 220, 360 − 220 = 140, so x = 140°

11. 11. ∠x = 66°

    Angles on a straight line make 180°: 180 − 114 = 66, so x = 66°

12. 12. ∠x = 45°

    A right angle is 90°: 90 − 45 = 45, so x = 45°

Part B: Word problems

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

1. 13. Three angles fit together round a point, making a full turn. Two of them are 80° and 138°. How many degrees is the third? (Answer: 142 degrees)

   360 − 80 − 138 = 142

2. 14. A right angle is split into two angles by a straight line. One of them is 56°. How many degrees is the other? (Answer: 34 degrees)

   90 − 56 = 34

3. 15. Three angles fit together round a point, making a full turn. Two of them are 114° and 145°. How many degrees is the third? (Answer: 101 degrees)

   360 − 114 − 145 = 101

4. 16. A right angle is split into two angles by a straight line. One of them is 63°. How many degrees is the other? (Answer: 27 degrees)

   90 − 63 = 27

5. 17. Two angles fit together to make a straight line. One is 47°. How many degrees is the other? (Answer: 133 degrees)

   180 − 47 = 133

6. 18. Two angles fit together to make a straight line. One is 132°. How many degrees is the other? (Answer: 48 degrees)

   180 − 132 = 48