Question

10 angle, which is four times its complement.
(i) Find the angles when two angles are supplementary and the
larger is 58° more than the smaller.
(ii) Two angles are supplementary and the larger is 40° less than three times the smaller, Find the
smaller angle.​

Answer 1

i) Let the angles be = x, y

x = y + 58

x + y = 180⁰ ( angles are supplementary)

y + 58 + y = 180

2y + 58 = 180

2y = 180 - 58

2y = 122

y = 122/2

y = 61⁰

x = 61 + 58 = 119

x = 119⁰ , y = 61⁰

ii) Let the angles be = x, y

x = 3y - 40

x + y = 180⁰ ( angles are supplementary)

3y - 40 + y = 180

4y - 40 = 180

4y = 180 + 40

4y = 220

y = 220/4

y = 55⁰

x = (3 × 55) - 40

x = 125⁰

x = 125⁰, y = 55⁰