The second angle in a triangle is five times as large as the first. The third angle is two-thirds as large as the first. Find the angle measures.

first angle: 27 degrees

second angle: 135 degrees

third angle: 18 degrees

Step-by-step explanation:

Represent each angle with a variable x and sum them to 180 degrees, the total angle measure of a triangle. So ...

first angle: x

second angle: 5x

third angle: 2x/3

x+5x+2x/3=180 Combine like terms

6x+2x/3=180 Change the 6x terms to have a denominator of 3

18x/3+2x/3=180 Combine like terms

20x/3=180 Cross multiply to solve for x

20x=540 so x=27

Now plug in to get angles:

first angle: 27

second angle: 135

third angle: 18

Check: 27+135+18=180