9-6 Finding Angle Measures in Polygons
Warm Up
Problem of the Day
Lesson Presentation
Course 1
9-6 Finding Angle Measures in Polygons
Warm Up
Solve.
1. n + 9 = 37
n = 28
2. 6 = n - 20
n = 26
3. 11n = 121
n = 11
4. 7 = n
7
n = 49
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9-6 Finding Angle Measures in Polygons
Problem of the Day
If a triangle has two angles that
measure 41° and 117°, what is the
measure of the third angle?
22°
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9-6 Finding Angle Measures in Polygons
Learn to find angle measures in polygons.
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9-6 Finding Angle Measures in Polygons
Additional Example 1: Subtracting to Find Angle
Measures
Use a protractor to find the measure of XYZ.
Then classify the angle.
Z
X
Y
• Place the center point of the protractor on
the vertex of the angle.
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9-6 Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ .
Then classify the angle.
Z
X
Y
• Read the measures where ray XY and ray YZ
cross.
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9-6 Finding Angle Measures in Polygons
Caution!
Ray XY can also be read as crossing at
30°, and ray YZ can be read at
crossing at 110°, The angle measure
is still the same. Make sure that you
read the measures on the same scale.
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9-6 Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ .
Then classify the angle.
Z
X
Y
• Ray XY crosses at 150°, and ray YZ crosses
at 70°.
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9-6 Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ .
Then classify the angle.
Z
X
Y
• The measure of XYZ is 150° - 70°, or
80°. Write this as mXYZ = 80°.
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9-6 Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ .
Then classify the angle.
Z
X
Y
• Since 80°< 90°, the angle is acute.
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9-6 Finding Angle Measures in Polygons
Additional Example 1 Continued
Use a protractor to find the measure of XYZ .
Then classify the angle.
Z
X
Check
Y
Use the other scale on the protractor to find the
measure of XYZ. 110° - 30° = 80°.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 1
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
M
• Place the center point of the protractor on
the vertex of the angle.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
M
• Read the measures where ray LM and ray MN
cross.
Course 1
9-6 Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
M
• Ray LM crosses at 50°, and ray MN crosses at
160°.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
M
• The measure of LMN is 160° - 50°, or
110°. Write this as m LMN = 110°.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
M
• Since 110° > 90°, the angle is obtuse.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN.
Then classify the angle.
L
N
Check
M
Use the other scale on the protractor to find the
measure of LMN. 130° - 20° = 110°.
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9-6 Finding Angle Measures in Polygons
To estimate the measure of an angle, compare it
with an angle whose measure you already know. A
right angle has half the measure of a straight
angle. A 45° angle has half the measure of a right
angle.
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9-6 Finding Angle Measures in Polygons
Additional Example 2: Estimating Angle
Measures
Estimate the measure of K in parallelogram
JKLM. Then use a protractor to check the
reasonableness of your answer.
M
L
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K
J
Think: The measure of
the angle is close to
150°.
9-6 Finding Angle Measures in Polygons
Additional Example 2 Continued
M
L
J
K
Use the protractor. The measure
Caution!
of the angle is 145°. mK =
145°, so the estimate is
Use the scale on the
reasonable.
protractor that
starts with 0°.
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 2
Estimate the measure of D in parallelogram
ABCD. Then use a protractor to check the
reasonableness of your answer.
A
B
Think: The measure of
the angle is close to
50°.
D
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C
9-6 Finding Angle Measures in Polygons
Check It Out: Example 2 Continued
A
D
B
C
Use the protractor. The measure of the angle is
53°. mD = 53°, so the estimate is reasonable.
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9-6 Finding Angle Measures in Polygons
Additional Example 3: Sports Application
The shape of a softball home plate is shown
below. Find the measures of C and E.
A
E
D
Use a protractor to
measure C.
B
C
CB crosses at 130°, and
CD crosses at 40°.
Subtract. 130° – 40° =
90°
C = 90°
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9-6 Finding Angle Measures in Polygons
Additional Example 3 Continued
The shape of a softball home plate is shown
below. Find the measures of C and E.
Estimate the mE.
A
E
B
It is greater than 90°, so
it looks as if the angle
measure is 90° + 45°.
So, mE is about 135°.
D
C
Use a protractor to
measure E.
E = 135°
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9-6 Finding Angle Measures in Polygons
Check It Out: Example 3
A quadrilateral is shown below. Find the
measures of A and C.
Use a protractor to
measure A.
A
B
D
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C
AB crosses at 40°, and
AD crosses at 110°.
Subtract. 110° - 40° =
70°
A = 70°
9-6 Finding Angle Measures in Polygons
Check It Out: Example 3 Continued
A quadrilateral is shown below. Find the
measures of A and C.
Estimate the mC.
A
B
D
C
It is greater than 90°, so
it looks as if the angle
measure is 90° + 20°.
So, mC is about 110°.
Use a protractor to
measure C.
C = 110°
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Measures
in Polygons
9-6 Finding
Insert Angle
Lesson
Title Here
Lesson Quiz: Part I
Solve each equation.
1. Use the protractor to the measure of ABC.
Tell what type of angle it is. 120°, obtuse
Course 1
Measures
in Polygons
9-6 Finding
Insert Angle
Lesson
Title Here
Lesson Quiz: Part II
Solve each equation.
2. Estimate the measure of B in the
parallelogram for Exercise 12 on page 512 of
your textbook. Then use a protractor to check
the reasonableness of your answer.
45°
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