Angles in Circles

Angles in Circles

How to find arcs/angles in a circle

Central angle: angle=arc

Central angles have a vertex at the center of the circle. The arc created by the two radii is equal to the angle.

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What is x?

Inscribed Angle: angle=1/2*arc or arc=2*angle

Inscribed angles must have a vertex touching the circle. The angle is half of the outside arc or the arc is twice the angle inside.

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What is x?

Two Tangents: angle+arc=180

Two tangents create an angle and an arc (small arc). These two added together always equal 180.

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What is x equal to?

External: angle=1/2(big arc - little arc)

When two secants meet outside of a circle, the angle is equal to half of the different of the arcs.

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What is the measure of the missing angle?

Internal: angle=1/2(big arc + little arc)

When two secants meet inside the circle, the angle is equal to half of the sum of the arcs.

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What is the measure of the internal angle?

Inscribed Quadrilateral: opposite angles =180

When a quadrilateral is inscribed in a circle, the opposite angles always add to 180.

Multiple Select

Select all equations that can be used to solve for x and y in the following inscribed quadrilateral.

• x+55=180

• y+85=180

• x+85=180

• y+55=180