Answer:
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 =
(GF + HL) , so
60 =
( 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°