Δ FGH is inscribed in the circle above. If arc FG is congruent to arc GH, and the measures of ∠ G is 30°, what is the measure of ∠ H?

The correct answer is: 75°

Hint:-
As per corollary to Inscribed Angles Theorem,
Angles inscribed with the same intercepted arc are equal.
Step-by-step solution:-
∠F & ∠H are inscribed with arcs GH & FG respectively, which are congruent to each other.
∴ ∠F = ∠H ----------- (Equation i)
Now, we know that-
Sum of all angles of a triangle = 180° -------- (Angle sum property)
∴ ∠F + ∠G + ∠H = 180°
∴ ∠H + ∠G + ∠H = 180° ---------- (From Equation i)
∴ ∠H + 30° + ∠H = 180°
∴ 2 × ∠H = 180° - 30°
∴ 2 × ∠H = 150°
∴ ∠H =
∴ ∠H = 75°
Final Answer:-
  Option C i.e. 75° is the correct Option.