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Transcript 
11-4
11-4Inscribed
InscribedAngles
Angles
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
11-4 Inscribed Angles
Warm Up
Find each value.
1. mBCA 63.5°
2. t 116.5°
Solve for x.
3. 58 – x = 4 (x + 7) 6
4. 2 (x – 8) = 8 12
Holt McDougal Geometry
11-4 Inscribed Angles
Objectives
Find the measure of an inscribed angle.
Use inscribed angles and their
properties to solve problems.
Vocabulary
inscribed angle
subtend
Holt McDougal Geometry
intercepted arc
11-4 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
11-4 Inscribed Angles
Holt McDougal Geometry
11-4 Inscribed Angles
Example 1A: Finding Measures of Arcs and Inscribed
Angles
Find each measure.
mPRU
mSP
Holt McDougal Geometry
11-4 Inscribed Angles
Check It Out! Example 1a
Find each measure.
mDAE
Holt McDougal Geometry
11-4 Inscribed Angles
Holt McDougal Geometry
11-4 Inscribed Angles
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°
Holt McDougal Geometry
11-4 Inscribed Angles
Check It Out! Example 2
Find mABD and mBC in the string art.
= 43
Holt McDougal Geometry
11-4 Inscribed Angles
Holt McDougal Geometry
11-4 Inscribed Angles
Finding Angle Measures in Inscribed Triangles
Find mLJM.
mLJM = mLKM
Find a.
WZY is a right angle
5b – 7 = 3b
mWZY = 90
2b – 7 = 0
5a + 20 = 90
5a = 70
a =14
Holt McDougal Geometry
.
2b = 7
b = 3.5
mLJM = 5(3.5) – 7 = 10.5
11-4 Inscribed Angles
Find z.
Find mEDF.
ABC is a right angle
mABC = 90
8z – 6 = 90
8z = 96
z = 12
Holt McDougal Geometry
mEDF = mEGF
2x + 3 = 75 – 2x
4x = 72
x = 18
mEDF = 2(18) + 3 = 39°
11-4 Inscribed Angles
Holt McDougal Geometry
11-4 Inscribed Angles
Example 4: Finding Angle Measures in Inscribed
Quadrilaterals
Find the angle measures of GHJK.
Step 1 Find the value of b.
Step 2 Find the measure
of each angle.
Holt McDougal Geometry
11-4 Inscribed Angles
Check It Out! Example 4
Find the angle measures of JKLM.
Holt McDougal Geometry
11-4 Inscribed Angles
Lesson Quiz: Part I
Find each measure.
1. RUS
2. a
25°
3
Holt McDougal Geometry
11-4 Inscribed Angles
Lesson Quiz: Part II
3. A manufacturer designs a
circular ornament with lines of
glitter as shown. Find mKJN.
130°
4. Find the angle measures of
ABCD.
m A = 95°
m B = 85°
m C = 85°
m D = 95°
Holt McDougal Geometry
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