Question

In ∆ ABC, the measures of the angles A, B, and C, respectively, are in the ratio 2:3:5.

What are the measures of the angles?

Answer 1

Let the measures of the angles be 2x, 3x, and 5x, where x is a constant. Since the sum of the angles in a triangle is 180 degrees, we have:

2x + 3x + 5x = 180

Simplifying the left side, we get:

10x = 180

Dividing both sides by 10, we get:

x = 18

Therefore, the measures of the angles are:

A = 2x = 2(18) = 36 degrees

B = 3x = 3(18) = 54 degrees

C = 5x = 5(18) = 90 degrees

So, the measures of the angles in ∆ABC are 36 degrees, 54 degrees, and 90 degrees.