word problem

Question

The third angle in an isosceles triangle is 20
more than 3
times as large as each of the two base angles. Find the measure of each angle.

Answer 1

Hi Ramon.

 

All three angles must sum to 180.

 

So the two base angles are the same, we will call them x.

 

The third angle then would be 20+ 3x

 

Adding all three angles we get

 

x + x + (20 + 3x) = 180

 

Combine like terms:

 

(x + x + 3x) + 20 = 180

 

5x + 20 = 180

 

 

Subtract 20 from both sides

 

5x = 160

 

Divide both sides by 5

 

x=32

 

So each base angle measures 32 degrees, 

and the third angle measures 32 * 3 + 20 = 116 degrees.

 

Check:  Does the sum of both base angles 

and the third angle = 180?

 

32 + 32 + 116 = 180   Got it!