1. Learning Targets I will find the measure of an inscribed angle.
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Learning Targets
I will find the measure of an inscribed angle.
I will use inscribed angles and their properties to solve problems.

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Vocabulary
inscribed angle
intercepted arc
subtend

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An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. A chord or arc subtends an angle if its endpoints lie on the sides of the angle.

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Remember: Central angles have the same measure as their intercepted arcs. Inscribed angles have measure that are one-half the measure of its intercepted arc.

5. Example 1A: Finding Measures of Arcs and Inscribed Angles
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Example 1A: Finding Measures of Arcs and Inscribed Angles
Find mPRU.

6. Example 1B: Finding Measures of Arcs and Inscribed Angles
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Example 1B: Finding Measures of Arcs and Inscribed Angles
Find
mSP

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8. Example 2: Hobby Application
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Example 2: Hobby Application
An art student turns in an abstract design for his art project.
Find mDFA.
mDFA = mDCF + mCDF
= 115°

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10. Example 3A: Finding Angle Measures in Inscribed Triangles
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Example 3A: Finding Angle Measures in Inscribed Triangles
Find a.
WZY is a right angle
mWZY = 90
5a + 20 = 90
5a = 70
a = 14

11. Example 3B: Finding Angle Measures in Inscribed Triangles
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Example 3B: Finding Angle Measures in Inscribed Triangles
Find mLJM.
mLJM = mLKM
5b – 7 = 3b
2b – 7 = 0
2b = 7
b = 3.5
mLJM = 5(3.5) – 7 = 10.5

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13. Example 4: Finding Angle Measures in Inscribed Quadrilaterals
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Example 4: Finding Angle Measures in Inscribed Quadrilaterals
Find the angle measures of GHJK.
Step 1 Find the value of b.
mG + mJ = 180
3b b + 20 = 180
9b + 45 = 180
9b = 135
b = 15

14. Step 2 Find the measure of each angle.
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Example 4 Continued
Step 2 Find the measure of each angle.
mG = 3(15) + 25 = 70
mJ = 6(15) + 20 = 110 .
mK = 10(15) – 69 = 81
mH + mK = 180
mH + 81 = 180
mH = 99