From the picture below, what is the measure of GC?

The measure of arc GC is 90°

Solution:

Given data:

m∠CHD = 90°

Sum of the adjacent angles in a straight line = 180°

⇒ m∠GHC + m∠CHD = 180°

⇒ m∠GHC + 90° = 180°

Subtract 90° from both sides, we get

⇒ m∠GHC = 90°

The angle measure of the central angle is equal to the measure of the intercepted arc.

90° = m(ar GC)

Switch the sides.

m(ar GC) = 90°

The measure of arc GC is 90°.

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