Question

The measure of an inscribed angle of circle is 65°, then what will be the measure of
central formed by intercepted arc of that inscribed angle?
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Answer 1

Answer:

The measure of intercepted arc is 130°

Step-by-step explanation:

From the Inscribed Angle Theorem we know that given the measure of the inscribed angle is half the measure of the intercepted arc.

An inscribed angle has its vertex on the circumference and the sides are two chords which intersect the circle to form the intercepted arc.

The intercepted arc will have the measure =  2 × 65° = 130°.

That is to say  m∠ADC  = $\frac{1}{2}$$\hat{AC}$.

Please see the figures attached for a complete explanation.