Question

An angle measures 74° less than the measure of a supplementary angle. What is the measure of each angle?

Answer 1

Answer:

One would be 90° and the other would be 16°

Answer 2

Answer:

Step-by-step explanation:

Call the measure of one angle n. The other angle, which is 74° less, measures n – 74°.

Since the angles are supplementary, their measures must add to 180°. Set up an equation and solve for n.

n

+  

n

−  74.0°

=  180.0°

2

n

−  74.0°

=  180.0°

2

n

−  74.0°

+  74.0°

=  

180.0°  +  74.0°

2

n

=  254.0°

2

n

÷  2

=  

254.0°  ÷  2

n

=  127.0°

The first angle measures 127°. Now plug in n = 127° to find the measure of the other angle, n – 74°.

n

−  74.0°

=  

127.0°  −  74.0°

=  53.0°

So, the two angles measure 127° and 53°.