Question

In triangle ABC, the measure of ∠B is two-third of the measure of ∠A. The measure of ∠C is 20° more than the measure of ∠A. Find the measures of the three angles.

Answer 1

Let angle ∠A be a°

Given that ∠B = `2/3 xx ∠"A" = 2/3"a"`

and given ∠C = ∠A + 20 = a + 20

Since A, B and C are angles of a triangle, they add up to 180° ...(∆ property)

∴∠A + ∠B + ∠C = 180°

⇒ `"a" + 2/3"a" + "a" + 20` = 180°

`(3"a" + 2"a" + 3"a")/3 + 20` = 180°

`(8"a")/3` = 180 – 20 = 160

∴ a =`(160 xx 3)/8` = 60°

∠B = `2/3 xx ∠"A" = 2/3 xx 60` = 40°

∠C = 80°