Question

21- Among two supplementary angles, the bigger angle is
40° more than the smaller angle. Find the measure of the smaller angle.
a) 60° b) 70°
c) 80°
d) 75°​

Answer 1

Given: Bigger angle is 40° more than the smaller one. Both are supplementary (make 180° in total).

To Find: Measurement of the smaller one.

We know,

Supplementary angles = 180°

(Complementary angles = 90°)

Let the smaller one be = N°

∴ Greater one = (N + 40)°

According to the Question:-

N° + (N + 40)° = 180°

→ N° + N° + 40° = 180°

→ 2N° = 180° - 40° = 140°

→ N° = 140°/2

→ N° = 70

∴ The smaller one was 70°.

Correct option: ☑ (b) 70°.

Verification (Not Required) :-

LHS:-

N° + (N + 40)°

= 70° + (70 + 40)°

= 70° + 110°

= 180°

RHS:-

180°

∴ LHS = RHS.