Answer:
The measure of ∠G is 59°
Step-by-step explanation:
When two secants, intersect at a point outside a circle then the measure of the angle formed between them is one-half the positive difference of the measures of the intercepted arcs.
In the given figure
∵ GT is a secant that intersects the circle at points H and T
∵ GE is a secant that intersects the circle at points F and E
∴ The intercepted arcs are HF and TE
∵ GT ∩ GE at G
∵ Point G is outside the circle
→ By using the rule above
∴ m∠G = [tex]\frac{1}{2}[/tex] (m arc TE - m arc HF)
∵ m arc TE = 175°
∵ m arc HF = 57°
→ Substitute them in the rule above
∵ m∠G = [tex]\frac{1}{2}[/tex] (175 - 57) = [tex]\frac{1}{2}[/tex] (118)
∴ m∠G = 59
∴ The measure of ∠G is 59°
