Question

The sum of the measures of a triangle is 180. The sum of the measures of the second and third angles of four times the measure of the first angle. The third angle is 12 less than the second

Answer 1

The correct answer is the 1st angle is 36 degrees, the 2nd angle is 78 degrees and the 3rd angle is 66 degrees.

Explanation:

First angle degrees = x

Second and third angles degrees = 4x (Four times the measure of the 1st)

x + 4x = 180

5x = 180

x = 180/5

x = 36

The 1st angle has 36 degrees of measure;

therefore, the sum of degrees of 2nd and 3rd angle is 144 (180 - 36)

Now, we can calculate the measure of the 2nd and 3rd angle using this formula:

2nd angle degrees = x

3rd angle degrees = x -12 (12 degrees less than the 2nd)

x + x - 12 = 144

2x - 12 = 144

2x = 156

x = 78

The 2nd angle has 78 degrees and the 3rd angle 66 degrees