Question

Need help on #15 please

Answer 1

Note that the angle whose measure is $(2x-12)^{\circ}$ is an exterior angle.

Thus, the sum of the measures of this exterior angle, and the 2 opposing interior angles is not 180°. 

It is the sum of the measure of its supplementary angle, and the other 2 opposing interior angles, which is equal to 180°.


So first, we find the measure of the supplementary angle (which is the third interior angle):

180°-(2x-12)°=180°-(2x)°+12°=192°-(2x)°.

Second, the sum of the measures of the interior angles is 180°, so:

192°-(2x)°+30°+x°=180°

192°-180°+30°=(2x)°-x°

42°=x°

So,  x=42.

The measure of the exterior angle is thus:
 
(2x-12)°=(2*42-12)°=(84-12)°=72°


Answer: 72°