Question 1

When an inscribed angle and a central angle share an arc, the inscribed angle is _________ of the central angle.

Question 2

Explanation:

$\textsf{We are asked for the relationship of a central angle and an inscribed angle when}$
$\textsf{these 2 angles share an arc.}$

$\large\underline{\textsf{What is a Central Angle?}}$

$\textsf{A \underline{central angle} is any angle connected by \underline{2 radiuses}.}$

$\large\underline{\textsf{What is an Inscribed Angle?}}$

$\textsf{An \underline{inscribed angle} is any angle \underline{insdie} of a circle. It's commonly connected to 3}$

$\textsf{points of the circumference, total.}$

$\textsf{Because they share an arc, the Inscribed Angle is less than the central angle.}$

$\large\underline{\textsf{How Much Less?}}$

$\textsf{It has always been proven that the Inscribed Angle is \underline{1/2} of the Central Angle if}$

$\textsf{they share an arc.}$

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