Question

Angle DEF is an inscribed angle on a circle, and m O 48° O 96° O 132° O 24°

Answer 1

∠24°

What is an inscribed angle in a circle?

Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc.

given that intercepted arc = ∠48°

The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.

If the intercepted arc is twice the size of the inscribed angle, then the inscribed angle is half the size of the intercepted arc. So if the intercepted arc is 48 degrees, the inscribed angle is 48 / 2 = 24 degrees.

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