Geometry 11-4 Inscribed Angles

1
Geometry 11-4 Inscribed Angles

• Inscribed angle- an angle whose vertex is on the
  circle.
• Intercepted arc- the arc in between the sides of
  the angle

AC is the intercepted arc
2
Theorem 1

• The inscribed angle is half the measure of the
  intercepted arc.

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Example

• Find each measure.

4
Example

• Find the value of a.

5
Example

• Determine the value of x.

(3x 20)
x
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Theorem 2

• If a quadrilateral is inscribed in a circle, then
  its opposite angles are supplementary.

7
Example

• Find the value of b.