Question

Please use the image below in order to find out the answer to the following question:

Find the measure of the red arc or angle.

What is the degree of m∠EHF?

Please show all the work on how you got your answer.

Answer 1

Given:

The measure of ∠EGF is 51°

We need to determine the measure of ∠EHF

Measure of ∠EHF:

By inscribed angle theorem, we know that, "if two inscribed angles of a circle intercept the same arc then the angles are congruent".

Applying the theorem, we have that the two inscribed angles of a circle intercepting the same arc are ∠G and ∠H

Then, the two angles are congruent.

Thus, we have;

∠G ≅ ∠H

Therefore, the measure of ∠G = ∠H = 51°

Hence, the measure of ∠EHF = 51°