The complete question is shown in the attached image
Answer: measure angle H = 42°
Explanation: There is a theorem that states that: "In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"
In the given, we have: angle E is an exterior angle to triangle DFH The two non-adjacent angles to angle E are angles D and H
Based on the above rule: measure angle E = measure angle D + measure angle H
We are given that: angle E = 87° angle D = 45°
Substitute with the givens in the above rule and solve for the measure of angle H as follows: angle E = angle D + angle H 87° = 45° + measure angle H measure angle H = 87° - 45° measure angle H = 42°
