Question

What is the value of the third angle of a triangle if the first two angles are in the ratio 4:5 ?

Answer 1

Given :

• The first two angles are in the ratio 4:5.

To find :

• The value of the third angle of triangle = ?

Step-by-step explanation :

Let, the third angle of the triangle be x.

Then, the first two angles are in the ratio be 4x and 5x.

As we know that :

Sum of all angles of triangle = 180°

So,

∠A + ∠B + ∠C = 180°

Substituting the values, we get,

➮ x + 4x + 5x = 180

➮ 10x = 180

➮ x = 180/10

➮ x = 18

Therefore, We get the value of x = 18°.

Hence,

The value of the third angle of triangle, x = 18°

The value of the second angle of triangle, 4x = 4 × 18 = 72°

The value of the first angle of triangle, 5x = 5 × 18 = 90°

Verification :

We know that,

Sum of all angles of triangle = 180°

So,

∠A + ∠B + ∠C = 180°

Substituting the values, we get,

18° + 72° + 90° = 180°

180° = 180°

LHS = RHS

Hence, it is verified.

Answer 2

Answer:

Given –

• Two angles of a triangle are in ratio of 4:5.

To Find –

• Third angle.

Solution –

Two angles of the triangle are 4x and 5x.

Let the third angle be x.

Hence, by angle sum property : 5x + 4x + x = 180°.

➸ 10x = 180

➸ x = 180/10

➸ x = 18°

Hence, the angles =

x = 18°

5x = 5*18 = 90°

and 4x = 4*18 = 72°

Hence, the angles of the traingle are 18°, 90° and 72°.

Let us verify our answer :

➸ 18° + 90° + 72°

➸ 180°

Hence, our answer is correct.