Finding measure of three angles with the third angle being 7/8 of the sum of the measures of the first two.

Question

The measure of two angles of a triangle are equal. The measure of the third angle is 7/8 of the sum of the measure of the first two angles. Find the measure of each angle.

Answer 1

For angles a, b, and c,
a+b+c=180 degrees
a=b
c=7/8 (2a)
Substitute b & c in terms of a, and solve it first
2a+14/8 a=180
16/8 a + 14/8 a=180
30a=180*8

a=b=48º
c=180-96=84º=7/8 of 96, so it checks out!

Answer 2

Let x represent one of the equal angles. Then,

 

2x+(7/8)(2x)=180

 

16x+14x=1440              (multiplied both sides by 8)

 

30x=1440

 

x=48

 

7x/8=42

 

So, two angles are 48 and the third angle is 42.