Question

Solve for x. And determine the measure of Arc GF

Answer 1

x = 10 , arc GF = 65°

Explanation:

the measure of the chord- chord angle GEF is half the sum of the arcs intercepted by the angle and its vertical angle, that is

∠ GEF =
`(1)/(2)` (GF + HL) , so

60 =
`(1)/(2)` ( 5x + 15 + 55) ← multiply both sides by 2 to clear the fraction

120 = 5x + 70 ( subtract 70 from both sides )

50 = 5x ( divide both sides by 5 )

10 = x

Then

arc GF = 5x + 15 = 5(10) + 15 = 50 + 15 = 65°