In triangle XYZ, m∠Y = 71.02° and m∠Z = 29.6°. Determine the measure of the exterior angle to ∠X.
a) 18.98°
b) 60.4°
c) 100.62°
d) 79.38°
The sum of the measures of the interior angles of a triangle is always 180°. Therefore, the measure of angle X is:
m∠X = 180° - m∠Y - m∠Z
m∠X = 180° - 71.02° - 29.6°
m∠X = 79.38°
The measure of the exterior angle to ∠X is equal to the sum of the measures of the two opposite interior angles. Therefore, the measure of the exterior angle to ∠X is:
m(exterior ∠X) = m∠Y + m∠Z
m(exterior ∠X) = 71.02° + 29.6°
m(exterior ∠X) = 100.62°
So the correct answer is:
c) 100.62°.