In triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6°. Determine the measure of the exterior angle to ∠X.
a 25.65°
b 41.25°
c 82.45°
d 97.55°
The sum of the measures of the angles in a triangle is 180°, so we can find the measure of ∠X by subtracting the measures of ∠Y and ∠Z from 180°.
∠X = 180° - 43.85° - 38.6°
∠X = 180° - 82.45°
∠X = 97.55°
The exterior angle to ∠X will be the sum of ∠Y and ∠Z, which is:
43.85° + 38.6° = 82.45°
Therefore, the correct answer is c) 82.45°.