Question

In the figure, three line segments cross at a common point. Angle A is 45°, and angle E is 85°. What is the measurement of angle F?

Answer 1

Answer: Measure angle H = 42°

Step-by-step explanation:

"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 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 this:

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°

Hope this helped!