Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Solve. 1. n 9 37 2. 6 n -
20 3. 11n 121 4. 7
n 28
n 26
n 11
n 7
n 49
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Problem of the Day If a triangle has two angles
that measure 41 and 117, what is the measure of
the third angle?
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Learn to find angle measures in polygons.
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Additional Example 1 Subtracting to Find Angle
Measures Use a protractor to find the measure of
?XYZ. Then classify the angle.
Y

• Place the center point of the protractor on the
  vertex of the angle.

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Additional Example 1 Continued Use a protractor
to find the measure of ?XYZ . Then classify the
angle.
Y

• Read the measures where ray XY and ray YZ cross.

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Additional Example 1 Continued Use a protractor
to find the measure of ?XYZ . Then classify the
angle.
Y

• Ray XY crosses at 150, and ray YZ crosses at 70.

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Additional Example 1 Continued Use a protractor
to find the measure of ?XYZ . Then classify the
angle.
Y

• The measure of ?XYZ is 150 - 70, or 80. Write
  this as m?XYZ 80.

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Additional Example 1 Continued Use a protractor
to find the measure of ?XYZ . Then classify the
angle.
Y

• Since 80lt 90, the angle is acute.

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Additional Example 1 Continued Use a protractor
to find the measure of ?XYZ . Then classify the
angle.
Check Use the other scale on the protractor to
find the measure of ?XYZ. 110 - 30 80.
Y
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Check It Out Example 1 Use a protractor to find
the measure of ?LMN. Then classify the angle.
M

• Place the center point of the protractor on the
  vertex of the angle.

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Check It Out Example 1 Continued Use a
protractor to find the measure of ?LMN. Then
classify the angle.
M

• Read the measures where ray LM and ray MN cross.

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Check It Out Example 1 Continued Use a
protractor to find the measure of ?LMN. Then
classify the angle.
M

• Ray LM crosses at 50, and ray MN crosses at 160.

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Check It Out Example 1 Continued Use a
protractor to find the measure of ?LMN. Then
classify the angle.
M

• The measure of ?LMN is 160 - 50, or 110. Write
  this as m ?LMN 110.

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Check It Out Example 1 Continued Use a
protractor to find the measure of ?LMN. Then
classify the angle.
M

• Since 110 gt 90, the angle is obtuse.

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Check It Out Example 1 Continued Use a
protractor to find the measure of ?LMN. Then
classify the angle.
Check Use the other scale on the protractor to
find the measure of ?LMN. 130 - 20 110.
M
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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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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.
Think The measure of the angle is close to 150.
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Additional Example 2 Continued
Use the protractor. The measure of the angle is
145. m?K 145, so the estimate is reasonable.
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Check It Out Example 2 Estimate the measure of
?D in parallelogram ABCD. Then use a protractor
to check the reasonableness of your answer.
Think The measure of the angle is close to 50.
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Check It Out Example 2 Continued
Use the protractor. The measure of the angle is
53. m?D 53, so the estimate is reasonable.
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Additional Example 3 Sports Application The
shape of a softball home plate is shown below.
Find the measures of ?C and ?E.
Use a protractor to measure ?C. CB crosses at
130, and CD crosses at 40. Subtract. 130 40
90
?C 90
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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. It is greater than 90, so it
looks as if the angle measure is 90 45. So,
m?E is about 135.
Use a protractor to measure ?E.
?E 135
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Check It Out Example 3 A quadrilateral is shown
below. Find the measures of ?A and ?C.
Use a protractor to measure ?A. AB crosses at
40, and AD crosses at 110. Subtract. 110 -
40 70
?A 70
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Check It Out Example 3 Continued A quadrilateral
is shown below. Find the measures of ?A and ?C.
Estimate the m?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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Insert 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
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Insert 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.
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