Question

In ∆ABC, the measure of angle A is equal to the sum of the measure of angle B and angel C. Also the ratio of measures of angle B and angel C is 4:5. Then find the measure of angles of the triangle.​

Answer 1

Answer:

The measures of the angles of the triangle are 90°, 40° & 50°.

Step-by-step-explanation:

We have given that,

The ratio of the measures of angle B and angle C of △ABC is 4 : 5.

Let the common multiple be x.

∴ m∠B = 4x

m∠C = 5x

Now, we have given that,

The measure of angle A is equal to the sum of the measures of the angles B & C.

∴ m∠A = m∠B + m∠C

⇒ m∠A = 4x + 5x

⇒ m∠A = 9x

Now, we know that,

The sum of measures of all angles of a triangle is 180°.

∴ m∠A + m∠B + m∠C = 180°

⇒ 9x + 4x + 5x = 180°

⇒ 13x + 5x = 180°

⇒ 18x = 180

⇒ x = 180 ÷ 18

⇒ x = 10°

Now,

Measure of angle A = 9x

⇒ Measure of angle A = 9 * 10

⇒ Measure of angle A = 90°

Now,

Measure of angle B = 4x

⇒ Measure of angle B = 4 * 10

⇒ Measure of angle B = 40°

Now,

Measure of angle C = 5x

⇒ Measure of angle C = 5 * 10

⇒ Measure of angle C = 50°

∴ The measures of the angles of the triangle are 90°, 40° & 50°.