Question

Circle R is shown. Tangents F G and H G intersect at point G outside of the circle to form an angle with a measure of 50 degrees. Point E is on the second arc. Arc F H has a measure of x degrees. In the diagram of circle R, m∠FGH is 50°. What is mAngle F E H? 130° 230° 260° 310°

Answer 1

if x = arc FG, then x = 130 degrees, the bigger arc is 230 degrees.

Explanation:

We see there are 2 tangent lines of circle R

There is a theorem that says angle FGH = [ (arc FEH) - (arc (FH)] /2

50 = (arc FEH - arc FH) /2

arc FEH - arc FH = 100

and arc FEH + arc FH = 360

solving this system you should get FH = 130 and FEH = 230