A

Mathematics

1 answer:

Juli2301 [7.4K]2 years ago

8 0

Answer:

20 degrees

Step-by-step explanation:

180-120-40=20

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In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H? 42°

Vinvika [58]

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°

Hope this helps :)