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12-4
12-4Inscribed
InscribedAngles
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Holt
12-4 Inscribed Angles
Learning Targets
I will find the measure of an inscribed
angle.
I will use inscribed angles and their
properties to solve problems.
Holt McDougal Geometry
12-4 Inscribed Angles
Vocabulary
inscribed angle
intercepted arc
subtend
Holt McDougal Geometry
12-4 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
12-4 Inscribed Angles
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.
Holt McDougal Geometry
12-4 Inscribed Angles
Example 1A: Finding Measures of Arcs and Inscribed
Angles
Find mPRU.
Holt McDougal Geometry
12-4 Inscribed Angles
Example 1B: Finding Measures of Arcs and Inscribed
Angles
Find mSP
Holt McDougal Geometry
12-4 Inscribed Angles
Holt McDougal Geometry
12-4 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
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
mWZY = 90
5a + 20 = 90
5a = 70
a = 14
Holt McDougal Geometry
12-4 Inscribed Angles
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
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
3b + 25 + 6b + 20 = 180
9b + 45 = 180
9b = 135
b = 15
Holt McDougal Geometry
12-4 Inscribed Angles
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
Holt McDougal Geometry
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12-4 Inscribed Angles
HOMEWORK:
Pages 824 – 825, #7 - 25
Holt McDougal Geometry