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

Answer:

The measure of each angle of Triangle is

∠ A = 60° ,

∠ B  =  30° ,

∠ C = 90°

Step-by-step 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  =  $\frac{180}{6}$

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