Question

In the diagram of circle R, m∠FGH is 50°. What is m? 130° 230° 260° 310°

Answer 1

we know that

The measurement of the exterior angle is the semi-difference of the arcs which comprises

In this problem

∠FGH is the exterior angle

∠FGH=$50\°$

∠FGH=$\frac{1}{2}(arc\ FEH-arc\ FH)$

$50\°=\frac{1}{2}(arc\ FEH-arc\ FH)$

$100\°=(arc\ FEH-arc\ FH)$  -----> equation A

$arc\ FEH+arc\ FH=360\°$

$arc\ FH=360\°-arc\ FEH$ --------> equation B

Substitute equation B in equation A

$100\°=(arc\ FEH-[360\°-arc\ FEH])$

$100\°=2arc\ FEH-360\°$

$2arc\ FEH=360\°+100\°$

$arc\ FEH=230\°$

therefore

The answer is

The measure of arc FEH is equal to $230\°$

Answer 2

The value of x from the diagram is 130 degrees

Angles and circles

From the given diagram;

Angle at the vertex is equal to half of the difference of angles at the arcs.

• 50 = 1/2(aecEFH - x)
• 100 = arc EFH - x ................  1

Similarly, arcEFH + x = 360

acEFH = 360 - x

Substitute into equation 3 into the result (1) to have:

100 =  360 - x - x ................  1

-260 = -2x

x = 130 degrees

Hence the value of x from the diagram is 130 degrees

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