Question

Two angles in a triangle are in the ratio 4 : 5 . If the sum of these angles is equal to the third angle , then find the smaller

Answer 1

Answer:

SOLUTION

Let the triangle (Δ) be ABC

Given : ∠A = 4x

∠B = 5x

∠C = ∠A+∠B

∠C= 4x + 5x = 9x

Here we use angle sum property

⇒ ∠A + ∠B + ∠C = 180°

⇒ 4x + 5x + 9x

⇒ 18x = 180°

⇒ x = \dfrac{180^\circ}{18}

18

180

∘

⇒ x = 10°

Let us verify that

to verify our answer we have to put 10° at the place of 'x'

let's do that

⇒ ∠A + ∠B + ∠C = 180°

⇒ 4x + 5x + 9x = 180°

⇒ 4×10 + 5×10 + 9×10 = 180°

⇒ 40 + 50 + 90 = 180°

⇒ 90 + 90 = 180°

⇒ 180° = 180°

∠A = 4x = 4×10 = 40°

∠B = 5x = 5×10 = 50°

∠C = ∠A+∠B

∠C= 4x + 5x = 9x = 9×10 = 90°

Therefore angles of triangle are 40° , 50° and 50°

Answer 2

Two angles in a triangle are in the ratio 4 : 5 .=40° ᵃⁿᵈ50°