Question

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles. Do not include the degree symbol in your answer

Answer 1

x=45 degrees

y=60 degrees

z=75 degrees

Explanation:

x+y+z=180

y+z=3x

So:

in x+(y+z) =180

x + 3x= 180

4x=180

x=180÷4

x=45 degrees

y+z=180-45=135

z is 15 more than y

y+y+15=135

2y+15=135

2y=120

y=120÷2=60 degrees

z=y+15=60+15=75 degrees