Question

The measure of an angle is seventeen times the measure of a supplementary angle. What is the measure of each angle?

Answer 1

Call the measure of one angle n. The other angle, which is seventeen times as big as n, measures 17n.

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

n

+  

17

n

=  180°

18

n

=  180°

18

n

÷  18

=  

180°  ÷  18

n

=  10°

The first angle measures 10°. Now plug in n = 10° to find the measure of the other angle, 17n.

17

n

=  

17  ×  10°

=  170°

So, the two angles measure 10° and 170°.

Got it

Answer 2

Supplementary angles are two angles that when add equal 180 degrees.
The supplement of an angle is 180 - n.

n = 17(180 - n)
n = 3060 - 17n
n + 17n = 3060
18n = 3060
n = 3060/18
n = 170

so the unknown angle (n) = 170 degrees and its supplement = (180 - 170 = 10)......= 10 degrees.