For , there is an exterior angle at vertex Z . If m = 68 ° and m = 47 ° , find m .
A)65 °
B)68 °
C)115 °
D)125 °

Question

For  , there is an exterior angle at vertex Z . If m  = 68 ° and m  = 47 ° , find m  .
A)65 ° 
B)68 ° 
C)115 ° 
D)125 °

Quizplus · Accepted Answer

The sum of the measures of the exterior angles of a polygon is always 360°. Therefore, the measure of angle Z is:

m 11ebfb55_249b_bc1e_9d86_b37374f4af0b_TBX8811_11 = 360° - (m 11ebfb55_249b_bc1c_9d86_373b9cff2021_TBX8811_11 + m 11ebfb55_249b_bc1d_9d86_5f3b0768afdd_TBX8811_11)

m 11ebfb55_249b_bc1e_9d86_b37374f4af0b_TBX8811_11 = 360° - (68° + 47°) = 245°

However, since 245° is an interior angle of the polygon, the exterior angle at vertex Z is:

180° - m 11ebfb55_249b_bc1e_9d86_b37374f4af0b_TBX8811_11 = 180° - 245° = 35°

Therefore, the correct answer is C) 115°, which is the supplement of the exterior angle.

For , There Is an Exterior Angle at Vertex