Question

The difference between two angles of a triangle whose magnitude is in the ratio 10 : 7 is 20° less than the third angle. The third angle is:

(a) 80°

(b) 56°

(c) 44°

(d) 70°

Answer 1

Correct option is (c) 44°

Let ∠A = 10x and ∠B = 7x

Given,  A − B = C − 20°

⇒ 10x − 7x = C − 20°

⇒ C = 3x + 20°

We know that sum of angles in a triangle = 180°

Therefore, 10x + 7x + 3x + 20° = 180°

⇒ 20x = 160°

⇒ x = 8°

Hence, ∠C = 3x + 20° = 44°