Question

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

Answer 1

Answer:

40° 50° 90°

Explanation:

et 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

Let the measure of two angles be 4x and 5x and the third one is ( 4x + 5x ).

We know that ;

Sum of angles of triangle = 180°

⇒ 4x + 5x + 4x + 5x = 180

⇒ 18x = 180

⇒ x = 180/18

⇒ x = 10

Therefore, the angles are ;

4x = 4 * 10 = 40°

5x = 5 * 10 = 50°

9x = 9 * 10 = 90°