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Transcript 
30.4 Inscribed
InscribedAngles
Angles
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
30.4 Inscribed Angles
Objectives
Find the measure of an inscribed angle.
Use inscribed angles and their
properties to solve problems.
Holt McDougal Geometry
30.4 Inscribed Angles
Vocabulary
inscribed angle
intercepted arc
subtend
Holt McDougal Geometry
30.4 Inscribed Angles
String art often begins with pins or nails that are
placed around the circumference of a circle. A long
piece of string is then wound from one nail to
another. The resulting pattern may include
hundreds of inscribed angles.
Holt McDougal Geometry
30.4 Inscribed Angles
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.
Holt McDougal Geometry
30.4 Inscribed Angles
Holt McDougal Geometry
30.4 Inscribed Angles
Example 1a
Find each measure.
mPRU
Inscribed  Thm.
Substitute 118 for mPU.
Holt McDougal Geometry
30.4 Inscribed Angles
Example 1b
Find each measure.
mSP
Inscribed  Thm.
Substitute 27 for m SRP.
Multiply both sides by 2.
Holt McDougal Geometry
30.4 Inscribed Angles
Example 2a
Find each measure.
Inscribed  Thm.
Substitute 135 for m ABC.
Multiply both sides by 2.
Holt McDougal Geometry
30.4 Inscribed Angles
Example 2b
Find each measure.
mDAE
Inscribed  Thm.
Substitute 76 for mDE.
Holt McDougal Geometry
30.4 Inscribed Angles
Holt McDougal Geometry
30.4 Inscribed Angles
Example 3
Find mABD and mBC in the string art.
Inscribed  Thm.
Substitute.
= 43
Inscribed  Thm.
Substitute.
Holt McDougal Geometry
30.4 Inscribed Angles
Holt McDougal Geometry
30.4 Inscribed Angles
Example 4
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.
30.4 Inscribed Angles
Example 5
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
30.4 Inscribed Angles
Holt McDougal Geometry
30.4 Inscribed Angles
Example 6
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
30.4 Inscribed Angles
Example 6 Continued
Step 2 Find the measure
of each angle.
mG = 3(15) + 25 = 70
Substitute 15 for b
mJ = 6(15) + 20 = 110
in each expression.
mK = 10(15) – 69 = 81
mH + mK = 180 H and K are supp.
mH + 81 = 180 Substitute 81 for mK.
mH = 99
Holt McDougal Geometry
Subtract 81 from both sides
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