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Transcript 
12-4
12-4Inscribed
InscribedAngles
Angles
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 Inscribed Angles
Objectives
Find the measure of an inscribed angle.
Use inscribed angles and their
properties to solve problems.
Holt McDougal Geometry
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 Inscribed Angles
Example 1A: Finding Measures of Arcs and Inscribed
Angles
Find each measure.
mPRU
Inscribed  Thm.
Substitute 118 for mPU.
Holt McDougal Geometry
12-4 Inscribed Angles
Example 1B: Finding Measures of Arcs and Inscribed
Angles
Find each measure.
mSP
Inscribed  Thm.
Substitute 27 for m SRP.
Multiply both sides by 2.
Holt McDougal Geometry
12-4 Inscribed Angles
Check It Out! Example 1a
Find each measure.
Inscribed  Thm.
Substitute 135 for m ABC.
Multiply both sides by 2.
Holt McDougal Geometry
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 Inscribed Angles
Check It Out! Example 2
Find mABD and mBC in the string art.
Inscribed  Thm.
Substitute.
= 43
Inscribed  Thm.
Substitute.
Holt McDougal Geometry
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 Inscribed Angles
Example 3A: Finding Angle Measures in Inscribed
Triangles
Find a.
WZY is a right angle WZY is inscribed in a semicircle.
mWZY = 90
Def of rt. 
5a + 20 = 90
Substitute 5a + 20 for mWZY.
5a = 70
a = 14
Holt McDougal Geometry
Subtract 20 from both sides.
Divide both sides by 5.
12-4 Inscribed Angles
Example 3B: Finding Angle Measures in Inscribed
Triangles
Find mLJM.
5b – 7 = 3b
mLJM and mLKM
both intercept LM.
Substitute the given values.
2b – 7 = 0
Subtract 3b from both sides.
mLJM = mLKM
2b = 7
b = 3.5
mLJM = 5(3.5) – 7 = 10.5
Holt McDougal Geometry
Add 7 to both sides.
Divide both sides by 2.
Substitute 3.5 for b.
12-4 Inscribed Angles
Check It Out! Example 3b
Find mEDF.
mEDF = mEGF
2x + 3 = 75 – 2x
4x = 72
x = 18
mEGF and mEDF
both intercept EF.
Substitute the given values.
Add 2x and subtract 3 from
both sides.
Divide both sides by 4.
mEDF = 2(18) + 3 = 39°
Holt McDougal Geometry
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 Inscribed Angles
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 GHJK is inscribed in a .
3b + 25 + 6b + 20 = 180 Substitute the given values.
9b + 45 = 180 Simplify.
9b = 135 Subtract 45 from both sides.
b = 15 Divide both sides by 9.
Holt McDougal Geometry
12-4 Inscribed Angles
Check It Out! Example 4
Find the angle measures of JKLM.
Step 1 Find the value of b.
mM + mK = 180 JKLM is inscribed in a .
4x – 13 + 33 + 6x = 180 Substitute the given values.
10x + 20 = 180 Simplify.
10x = 160 Subtract 20 from both sides.
x = 16 Divide both sides by 10.
Holt McDougal Geometry
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