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9-6
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9-6 Finding Angle Measures in Polygons Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day
description
9-6. Finding Angle Measures in Polygons. Course 1. Warm Up. Problem of the Day. Lesson Presentation. 9-6. Finding Angle Measures in Polygons. Course 1. Warm Up Solve. 1. n + 9 = 37 2. 6 = n - 20 3. 11 n = 121 4. 7 = . n = 28. n = 26. n = 11. n 7. n = 49. - PowerPoint PPT Presentation
Transcript of 9-6
9-6 Finding Angle Measures in Polygons
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpSolve.
1. n + 9 = 37
2. 6 = n - 20
3. 11n = 121
4. 7 =
n = 28
n = 26
Course 1
9-6 Finding Angle Measures in Polygons
n = 11
n = 49n 7
Problem of the Day
If a triangle has two angles that measure 41° and 117°, what is the measure of the third angle?22°
Course 1
9-6 Finding Angle Measures in Polygons
Learn to find angle measures in polygons.
Course 1
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.
Course 1
9-6 Finding Angle Measures in Polygons
• Place the center point of the protractor on the vertex of the angle.
Y
X
Z
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
• Read the measures where ray XY and ray YZ cross.
Y
X
Z
Course 1
9-6 Finding Angle Measures in Polygons
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.
Caution!
Course 1
9-6 Finding Angle Measures in Polygons
• Ray XY crosses at 150°, and ray YZ crosses at 70°.
Y
X
Z
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
Y
X
Z
• The measure of XYZ is 150° 70°, or 80°. Write this as mXYZ = 80°.
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
Y
X
Z
• Since 80°< 90°, the angle is acute.
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
Y
X
Z
Check
Use the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°.
Additional Example 1 Continued
Use a protractor to find the measure of XYZ . Then classify the angle.
Check It Out: Example 1
Use a protractor to find the measure of LMN. Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
• Place the center point of the protractor on the vertex of the angle.
M
N
L
Course 1
9-6 Finding Angle Measures in Polygons
• Read the measures where ray LM and ray MN cross.
N
L
M
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
• Ray LM crosses at 50°, and ray MN crosses at 160°.
N
L
M
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
M
N
L
• The measure of LMN is 160° 50°, or 110°. Write this as m LMN = 110°.
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
M
N
L
• Since 110° > 90°, the angle is obtuse.
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
M
N
L
Check
Use the other scale on the protractor to find the measure ofLMN. 130° - 20° = 110°.
Check It Out: Example 1 Continued
Use a protractor to find the measure of LMN. Then classify the angle.
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.
Course 1
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.
Think: The measure of the angle is close to 150°.
Course 1
9-6 Finding Angle Measures in Polygons
L
M J
K
Additional Example 2 Continued
Use the protractor. The measure of the angle is 145°. mK = 145°, so the estimate is reasonable.
Use the scale on the protractor that starts with 0°.
Caution!
Course 1
9-6 Finding Angle Measures in Polygons
L
M J
K
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°.
Course 1
9-6 Finding Angle Measures in Polygons
D
A B
C
Check It Out: Example 2 Continued
Use the protractor. The measure of the angle is 53°. mD = 53°, so the estimate is reasonable.
Course 1
9-6 Finding Angle Measures in Polygons
D
A B
C
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°
Course 1
9-6 Finding Angle Measures in Polygons
A
BE
CD
C = 90°
Additional Example 3 Continued
The shape of a softball home plate is shown below. Find the measures of C and E.
Estimate the mE.
It is greater than 90°, so it looks as if the angle measure is 90° + 45°.
So, mE is about 135°.
Course 1
9-6 Finding Angle Measures in Polygons
A
BE
CDUse a protractor to measure E.
E = 135°
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°
Course 1
9-6 Finding Angle Measures in Polygons
A = 70°
A B
CD
Check It Out: Example 3 Continued
A quadrilateral is shown below. Find the measures of A and C.
Estimate the mC.
It is greater than 90°, so it looks as if the angle measure is 90° + 20°.
So, mC is about 110°.
Course 1
9-6 Finding Angle Measures in Polygons
Use a protractor to measure C.
C = 110°
A B
CD
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
Insert Lesson Title Here
Course 1
9-6 Finding Angle Measures in Polygons
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.
Insert Lesson Title Here
45°
Course 1
9-6 Finding Angle Measures in Polygons
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