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

Mathematics

2 answers:

omeli [17]4 years ago

6 0

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

<u>The answer is</u>

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

Ulleksa [173]4 years ago

4 0

Answer:

B is the answer

Step-by-step explanation:

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