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 exterior angles of any triangle is always 360°.
Since the sum of the measures of the interior angles of triangle XYZ is 180° (as in any triangle), we can find the measure of angle X by subtracting the sum of angles Y and Z from 180°:
m∠X = 180° - (m∠Y + m∠Z)
m∠X = 180° - (43.85° + 38.6°)
m∠X = 180° - 82.45°
m∠X ≈ 97.55°
Therefore, the measure of the exterior angle to ∠X is also 97.55°.
Answer: d) 97.55°