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nlexa [21]
3 years ago
5

What is the measure of

Mathematics
1 answer:
Sever21 [200]3 years ago
8 0

Answer:

The measure of ∠G is 59°

Step-by-step explanation:

<em>When </em><em>two secants</em><em>, intersect at </em><em>a point outside a circle</em><em> then the </em><em>measure of the angle formed between them</em><em> is </em><em>one-half the positive difference of the measures of the intercepted arcs.</em>

<em></em>

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 = \frac{1}{2} (m arc TE - m arc HF)

∵ m arc TE = 175°

∵ m arc HF = 57°

→ Substitute them in the rule above

∵ m∠G = \frac{1}{2} (175 - 57) = \frac{1}{2} (118)

∴ m∠G = 59

∴ The measure of ∠G is 59°

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