Final answer:
To find the measure of the exterior angle at vertex G of triangle EFG, we sum the measures of the other two angles, ∠E and ∠F, which results in an exterior angle measure of 102.5°.
Step-by-step explanation:
The question asks us to determine the measure of the exterior angle at vertex G of triangle EFG. Since the sum of the interior angles in any triangle is always 180°, we first need to find the measure of ∠G by subtracting the measures of ∠E and ∠F from 180°.
m∠G = 180° - m∠E - m∠F
= 180° - 73.9° - 28.6°
= 180° - 102.5°
= 77.5°
Now, to find the measure of the exterior angle at G, which is the exterior angle to ∠G, we use the fact that an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. In this case, the exterior angle at G will be equal to m∠E + m∠F.
m∠(G exterior) = m∠E + m∠F
= 73.9° + 28.6°
= 102.5°
Therefore, the measure of the exterior angle at G is 102.5°, which corresponds to option C.