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The Inscribed Angle Theorem tells us that the measure of an inscribed angle is half the measure of its intercepted arc.
46^(∘)
An angle whose vertex is on a circle and whose sides are chords of the circle is an inscribed angle. Therefore, in the given diagram the angle with a measure of 23^(∘) is an inscribed angle. We want to find the measure of the intercepted arc TU.
Let's recall the Inscribed Angle Theorem.
Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
This means that the measure of the intercepted arc must be twice the measure of the inscribed angle. mTU=2* 23^(∘)= 46^(∘)
