Question

What is the measure of

Answer 1

The measure of ∠G is 59°

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 =
`(1)/(2)` (m arc TE - m arc HF)

∵ m arc TE = 175°

∵ m arc HF = 57°

→ Substitute them in the rule above

∵ m∠G =
`(1)/(2)` (175 - 57) =
`(1)/(2)` (118)

∴ m∠G = 59

∴ The measure of ∠G is 59°