Find the measures of the three angles.

Question

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 twice the measure of the first angle. The third angle is 12 more than the second.

Answer 1

Number the angles A1, A2 & A3

 (1) A1 + A2 + A3 = 180

(2)  A2 + A3 = 2A1

(3) A3 = A2 + 12

 

Rearrange these equations as follow

(1) A1 + A2 + A3 = 180

(2) -2A1 + A2 + A3 = 0

(3) -A2 + A3 = 12

 

Multiply equation (1) by 2 andadd equation (1) to equation (2)

(1) + (2) 3A2 + 3A3 = 360

Divide this by 3 and call it equation (4)

 

(4) A2 + A3 = 120

(3) -A2 + A3 = 12

Add them to get

 

2A3 = 132

A3 = 66

 

from equation (3) A2 = A3 - 12 = 66 - 12 = 54

 

from equation (1) A1 = 180 - A2 - A3 = 180 - 54 - 66 = 60

 

Now go back and check that these answers, in fact, solve your problem.