Question

14. One of the angles of a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 1:2, find the angles of the triangle.​

Answer 1

Given:

One of the angles of a triangle = Sum of other two angles and the ratio of other two angles is 1:2.

To find:

We've o find the angles of the triangle.

Required answer:

The three angles of the triangle are 90°,30° and 60°.

Explaination:

According to the question :

➨ ∠1 = ∠2 + ∠3

➨ ∠1 = x + 2x

➨ ∠1 = 3x

Wee know that sum of all the angles in a triangle is 180°. So :

➨ ∠1 + ∠2 + ∠3 = 180°

➨ 3x + x + 2x = 180°

➨ 6x = 180°

➨ x = 180/6

➨ x = 30

Let's substitute niw and find the angles individually :

➨ ∠1 = 3x = 90°

➨ ∠2 = x = 30°

➨ ∠3 = 2x = 60°

Verification:

Let's add all the angles and verify whether they add upto 180° or not :

➨ ∠1 + ∠2 + ∠3 = 180°

➨ 90° + 30° + 60° = 180°

➨ 90° + 90° = 180°

➨ 180° = 180°

➨ LHS = RHS

Henceforth, verified!