Question

The circle below has a center H. Suppose that m FG=42. Find the following.

Answer 1

The measure of angle FHG = 42 degrees. This is the same as the arc length.

The measure of angle FEG = 21 degrees. This is half the value of the arc length.

Answer 2

The measure of angles are

$m < FHG= 42\\m < FEG= 21$

Central angle :

Central angle is equal to intercepted arc.

Also, inscribed angle  is equal to half of the intercepted arc.

From the given diagram ,

Central angle is angle FHG.

Given that measure of Arc FG = 42 degrees

Central angle = intercepted arc

Central angle is same as intercepted arc.

$m < FHG= m (arc FG)\\m < FHG= 42$

Inscribed angle  is equal to half of the intercepted arc.

To find inscribed angle , we divide the intercepted arc by 2.

$m < FEG=\frac{1}{2} (arc FG)\\m < FEG=\frac{1}{2} (42)\\m < FEG= 21$

The following angles are

$m < FHG= 42\\m < FEG= 21$

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