The measure of one angle is six more than half the measure of another angle. If the angles are complementary, find both measures.

Question

I'm totally lost!!

Answer 1

The angles are complementary means they add to 90°

A is the first angle and B, the second angle, is (A/2) + 6.

A + B = 90 

Substitute:

A + [(A/2) + 6]  = 90

Clear fractions:

2A + A + 12 = 180

Collect:

3A = 168

A = 56

and B = (A/2) + 6 = 34

Check: 56 + 34 = 90

Answer 2

Let x = one of the angles.  The second angle is 6 more than half of x: x/2 + 6.  Since the two angles are complementary, they sum to 90°.

 

x + x/2 + 6 = 90

3x/2 + 6 = 90

3x/2 = 84

 

Solve for x.  The first angle is x, the second is x/2 + 6.  Check to be sure they sum to 90°