b Let's highlight the rays that create ∠ 4 and ∠ 7.
As we can see, both of the green rays are opposite rays with a blue ray. Therefore, ∠ 4 and ∠ 7 are vertical angles. According to the Vertical Angles Congruence Theorem, they are congruent.
∠ 4 ≅ ∠ 7
However, we are supposed to relate the measure of each of the angles. By the Definition of Congruent Angles, the measures are equal.
m∠ 4 = m∠ 7
c Let's highlight the rays that create ∠ FHE and ∠ AHG.
Since ∠ FHE is a right angle and ∠ AHG appears to be less than 90^(∘), the angles cannot be congruent. If the angles are not congruent, their measures cannot be equal.
m∠ FHE ≠ m∠ AHG
d Let's highlight the rays that create ∠ AHG and ∠ GHE.
The two angles are adjacent with noncommon sides that form opposite rays. This means we can classify them as a linear pair. By the Linear Pair Postulate, we know they are supplementary and their measures add up to 180^(∘).
m∠ AHG + m∠ GHE = 180^(∘)
