In triangle EFG, m∠E = 69.7° and m∠F = 25.9°. Determine the measure of the exterior angle to ∠G.
a) 43.8°
b) 84.4°
c) 110.3°
d) 95.6°
The sum of the interior angles in a triangle is always 180°. So, if we subtract the measures of ∠E and ∠F from 180°, we can find the measure of ∠G.
180° - 69.7° - 25.9° = 84.4°
Since ∠G is an exterior angle to ∠EFG, the measure of the exterior angle is equal to the sum of the remote interior angles. In this case, the remote interior angles are ∠E and ∠F, so the measure of the exterior angle is 69.7° + 25.9° = 95.6°.
Therefore, the measure of the exterior angle to ∠G is 95.6°.
The correct answer is (d) 95.6°.