In triangle XYZ, m∠Y = 45.43° and m∠Z = 38.7°. Determine the measure of the exterior angle to ∠X.
a 44.57°
b 51.3°
c 75.75°
d 84.13°
The sum of the angles in a triangle is always 180°. We can use this fact to find the measure of angle X.
m∠Y + m∠Z + m∠X = 180°
Plugging in the given values:
45.43° + 38.7° + m∠X = 180°
Adding the angles on the left side:
84.13° + m∠X = 180°
To isolate m∠X, we subtract 84.13° from both sides:
m∠X = 180° - 84.13°
m∠X = 95.87°
The exterior angle to ∠X is equal to the sum of the remote interior angles, which is 180° - m∠X.
Exterior angle = 180° - 95.87°
Exterior angle = 84.13°
Therefore, the measure of the exterior angle to ∠X is 84.13°.
The correct answer is d) 84.13°.