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

Question

Jaxon Michael

Mathematics

10 September, 08:10

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

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Answers (1)

Know the Answer?

Malachi Larson · Answer 1

x=45 degrees

y=60 degrees

z=75 degrees

Step-by-step 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