Angles in triangles and quadrilaterals worksheet

Part A: Working out and filling in

1. 1. Isosceles triangle: ∠x = 80°

   An isosceles triangle's two base angles are equal: 180 − 20 = 160, shared by the two: 160 ÷ 2 = 80, so x = 80°

2. 2. Triangle: ∠x = 40°

   A triangle's three angles make 180°: add the angles you know first, 49 + 91 = 140, 180 − 140 = 40, so x = 40°

3. 3. Right-angled trapezium: ∠x = 61°

   A quadrilateral's four angles make 360°, two of them right angles: 90 + 90 = 180, 180 + 119 = 299, 360 − 299 = 61, so x = 61°

4. 4. Isosceles triangle: ∠x = 65°

   An isosceles triangle's two base angles are equal: 180 − 50 = 130, shared by the two: 130 ÷ 2 = 65, so x = 65°

5. 5. Right-angled trapezium: ∠x = 75°

   A quadrilateral's four angles make 360°, two of them right angles: 90 + 90 = 180, 180 + 105 = 285, 360 − 285 = 75, so x = 75°

6. 6. Quadrilateral: ∠x = 60°

   A quadrilateral's four angles make 360°: add the angles you know first, 85 + 95 = 180, 180 + 120 = 300, 360 − 300 = 60, so x = 60°

7. 7. Triangle: ∠x = 75°

   A triangle's three angles make 180°: add the angles you know first, 29 + 76 = 105, 180 − 105 = 75, so x = 75°

8. 8. Right-angled triangle: ∠x = 55°

   A triangle's three angles make 180°, one of them a right angle, 90°: 90 + 35 = 125, 180 − 125 = 55, so x = 55°

9. 9. Triangle: ∠x = 100°

   A triangle's three angles make 180°: add the angles you know first, 45 + 35 = 80, 180 − 80 = 100, so x = 100°

10. 10. Isosceles triangle: ∠x = 48°

    An isosceles triangle's two base angles are equal: 180 − 84 = 96, shared by the two: 96 ÷ 2 = 48, so x = 48°

11. 11. Isosceles triangle: ∠x = 42°

    An isosceles triangle's two base angles are equal: 180 − 96 = 84, shared by the two: 84 ÷ 2 = 42, so x = 42°

12. 12. Quadrilateral: ∠x = 120°

    A quadrilateral's four angles make 360°: add the angles you know first, 60 + 110 = 170, 170 + 70 = 240, 360 − 240 = 120, so x = 120°

Part B: Word problems

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

1. 13. One of the acute angles of a right-angled triangle is 29°. How many degrees is the other acute angle? (Answer: 61 degrees)

   180 − 90 − 29 = 61

2. 14. Two angles of a triangle are 82° and 31°. How many degrees is the third angle? (Answer: 67 degrees)

   180 − 82 − 31 = 67

3. 15. One of the acute angles of a right-angled triangle is 46°. How many degrees is the other acute angle? (Answer: 44 degrees)

   180 − 90 − 46 = 44

4. 16. The angle at the top of an isosceles triangle is 136°. How many degrees is each of its base angles? (Answer: 22 degrees)

   (180 − 136) ÷ 2 = 22

5. 17. Two angles of a triangle are 34° and 39°. How many degrees is the third angle? (Answer: 107 degrees)

   180 − 34 − 39 = 107

6. 18. The angle at the top of an isosceles triangle is 126°. How many degrees is each of its base angles? (Answer: 27 degrees)

   (180 − 126) ÷ 2 = 27