Question

The second angle of a triangle is three times the first, and the third is 12 degrees less than twice the first. Find the measure of the angles.

Answer 1

32°, 96° and 52°

Explanation:

The sum of the angles of a triangle will always measure 180°. In the case of this triangle, we can form three expressions using the same variable and add them together to equal 180.

first angle = x

second angle = 3x (three times the first)

third angle = 2x - 12 (12 degrees less than twice the first)

Combine and set them equal to 180:

x + 3x + 2x - 12 = 180 or 6x - 12 = 180

Add 12 to both sides: 6x - 12 + 12 = 180 + 12 or 6x = 192

Divide by 6 and solve for 'x': 6x/6 = 192/6 or x = 32

first angle = 32°

second angle = 3x = 96°

third angle = 2x - 12 = 52°