Solve using systems

Question

The sum of the measures of the angles of any triangle is 180°. In ABC, Angle A measures 100° less than the sum of the measures of Angle B and Angle C, and the measure of Angle C is 40° less than twice the measure of Angle B. Find the measure of each angle of the triangle. 

Answer 1

A + B + C = 180  (1)

A = B + C - 100   (2)

C = 2B - 40         (3)

 

Rewrite equation (2) as   A - B - C = -100   (4)

 

Add equations (1) and (4) to get

 

2A = 80  ==>  A = 40

 

Plug this in to equation (1) to get 

 

B + C = 140  (5)

 

Plug the value for C from equation (3) in to equation (5) 

 

B + (2B - 40) = 140

3B = 180

B = 60 

 

C = 140 - B = 140 - 60 = 80

 

A = 40 degrees, B = 60 degrees, C = 80 degrees