Question

The measure of one of the angles of a triangle is twice the measure of its smallest
angle and the measure of the other is thrice the measure of the smallest angle. Find the
measures of the three angles.​

Answer 1

Answer :-

Angles of triangle are 30° , 60° , and 90°

Step-by-step explanation:

To Find :-

Measures of the three angles.​

Solution :-

Let the smallest angle be = x

Then, according to question 2nd angle = 2x

and 3rd angle = 3x

We know that in a triangle sum of all angles = 180°

So,

x + 2x + 3x = 180

6x = 180

x = 180 / 6 = 30

x = 30

Finding the three angles :-

smallest angle = x = 30°

2nd angle = 2x = 2(30) = 60°

3rd angle = 3x = 3(30) = 90°

Answer 2

let angle be A,B,C respectively.

let smallest angle be B=x

then first angle A=2x

and the other angle C=3x

According to question:

A+B+C=180°

2x+x+3x=180°

6x=180°

x=180°÷6

x=30°

Now angle B=x=30°

A=2x=2×30°=60°

C=3x=3×30°=90°

Hence, Angles are respectively A=60°,B=30°and C=90°