Question

The angles of a triangle add up to 180 degrees.

The second angle is 20 degrees larger than the smallest angle.
The third angle is 3 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).

Answer 1

32 degrees

Explanation:

You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.

Setup

The sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...

x +(x +20) +3x = 180

Solution

Collecting terms gives ...

5x +20 = 180

5x = 160 . . . . . . subtract 20

x = 32 . . . . . . divide by 5

The smallest angle is 32 degrees.