Summary of equations

Question

The sum of the measures of angle A and Angle B is 90. Angle A is 30 less than twice angle B. What are the system of equations and solve them.

Answer 1

The sum of the measures of angle A and Angle B is 90:

 

     A + B = 90

 

Angle A is 30 less than twice angle B:

 

     A = 2B - 30

 

In the first equation, substitute 2B - 30 in place of A:

 

     A + B = 90

     2B - 30 + B = 90

     3B - 30 = 90

     3B = 120

     B = 40°

 

     A = 2B - 30

     A = 2(40) - 30

     A = 80 - 30

     A = 50°