Question

Find the measure of each angle and classify the triangle accordingly. In triangle ABC, measure of angle A = 2(measure of angle B) and measure of angle C = 3(measure of angle B).

Answer 1

The measure of each angle of Triangle is

∠ A = 60° ,

∠ B = 30° ,

∠ C = 90°

Explanation:

Given as in a triangle :

The three angles of Triangle are

∠ A , ∠ B , ∠ C

∠ A = 2 × ∠ B

∠ C = 3 × ∠ B

Now, From the property of Triangle

The sum of all the three angles of Triangle is 180°

So, ∠ A + ∠ B + ∠ C = 180°

Or, ( 2 × ∠ B ) + ∠ B + ( 3 × ∠ B ) = 180°

Or, 6 × ∠ B = 180°

∴ ∠ B =
`(180)/(6)`

So, ∠ B = 30°

And , ∠ A = 2 × ∠ B = 2 × 30°

So, ∠ A = 60°

Similarly , ∠ C = 3 × ∠ B = 3 × 30°

So, ∠ C = 90°

Hence The measure of each angle of Triangle is ∠ A = 60° , ∠ B = 30° ,

∠ C = 90° Answer