Answer:
if x = arc FG, then x = 130 degrees, the bigger arc is 230 degrees.
Step-by-step 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
The measure of ∠FEH is 55°
"It is a line which intersects the circle at only one point."
"It is the segment of the circumference of a circle."
For given example,
Consider the figure shown below.
∠FGH = 50°
Arc FH has a measure of x°.
⇒ ∠FRH = x°
We know, "the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtended by the line segment."
⇒ ∠FGH + ∠FRH = 180°
⇒ 50° + x° = 180°
⇒ x° = 180° - 50°
⇒ x° = 130°
Point E is on the second arc.
We need to find measure of ∠FEH.
We know, "the measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc."
⇒ ∠FRH = 2 × ∠FEH
⇒ 130 = 2 × ∠FEH
⇒ ∠FEH = 130/2
⇒ ∠FEH = 55°
Therefore, the measure of ∠FEH is 55°
Learn more about a circle here:
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