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.

Question

This is on angles in triangles.

8th grade pre-algebra, geometry chapter. 

Answer 1

For angles a, b and c in the interior of a triangle, we know that a + b + c = 180

 

The question tells us b = 5a and that c = (2/3)*a

 

substitute the second and third equations into the first:

 

a + 5a + (2/3)a = 180

 

20/3 * a = 180

 

a = 27

 

Substitute this result back into the second and third equations to get b = 5a = 5*27 = 135   and c = (2/3)*27 = 18

 

Double checking 27 + 18 + 135 = 180.