I need help please

Question

Two angles are complementary. Twice one angle plus the other is 148°. Find the measure of each angle. 

Answer 1

To solve this problem, set up the angles as a system of equation.  You know that angle one (a) plus angle two (b) equals 90 degrees. This is the first equation.  The other comes from twice of one angle (in this case we can use angle one or two) and the other added is 148 degrees.  So, your system should look like this:

 

a + b = 90

2a + b = 148

 

Now you can solve this system for both angles using either substitution or elimination.  If you use elimination, multiply the first equation by the coefficient -1 and add it to the other to get this relationship:

 

-a + -b = -90

2a + b = 148

 

a = 58

 

So, angle one (a) is equal to 58 degrees.  Now you can plug this into the first equation and see that angle two (b) is equal to 32 degrees.