Inscribed Angles and Arc Length

A circle has an inscribed angle that intercepts an arc measuring 150 degrees. What is the measure of the inscribed angle?

• 75 degrees

• 150 degrees

• 225 degrees

• 300 degrees

Answer explanation

The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, the inscribed angle measures 75 degrees (150 degrees / 2 = 75 degrees).

Tags

CCSS.HSG.C.A.2

In a circle, two inscribed angles that subtend the same arc are measured. If one angle is 45 degrees, what is the measure of the other angle?

• 45 degrees

• 90 degrees

• 135 degrees

• 180 degrees

Answer explanation

This is an example explanation.

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CCSS.HSG.C.A.2

Find the measure of arc AB.

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CCSS.HSG.C.A.2

What is the measure of arc NM?

• 116

• 117

• 118

• 119

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CCSS.HSG.C.A.2

An inscribed angle in a circle subtends an arc of 100 degrees. What is the measure of the inscribed angle?

• 50 degrees

• 100 degrees

• 150 degrees

• 200 degrees

Answer explanation

The measure of an inscribed angle is half the measure of the arc it subtends. Therefore, the inscribed angle measures 50 degrees (100 degrees / 2 = 50 degrees).

Tags

CCSS.HSG.C.A.2

In the diagram, quadrilateral PQRS is inscribed in circle O. Match each statement with the correct value.

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CCSS.HSG.C.A.2

Find the measure of arc BC

• 24^o

• 156^o

• 56^o

• 180^o

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CCSS.HSG.C.B.5

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

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CCSS.HSG.C.B.5

Match the following

• If a quadrilateral is inscribed in a circle, then its opposite angles add up to 180⁰

• Inscribed Quadrilateral Theorem

• Angles that are opposite each other and formed by two intersecting straight lines, are congruent.

• Inscribed Angle of a Diameter Theorem

• The measure of an inscribed angle is equal to half the measure of its intercepted arc.

• Arc Additional Postulate

• The measure of an arc formed by two adjacent arcs is the sum of the measure of the two arcs.

• Inscribed Angle Theorem

• The endpoints of a diameter lie on an inscribed angle if & only if they inscribed angle is 90⁰

• Vertical Angles Theorem

Tags

CCSS.HSG.C.A.2

The distance between endpoints of an arc measured in linear units

• Point of Tangency

• Arc

• Chord

• Arc Length