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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? 22° Course Finding Angle Measures in Polygons
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9-6 Finding Angle Measures in Polygons
Course 1
Warm UpWarm Up
Lesson PresentationLesson PresentationProblem 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 DayIf 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
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 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 ContinuedUse 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 ContinuedUse a protractor to find the measure of XYZ . Then classify the angle.
Course 1
9-6 Finding Angle Measures in Polygons
Y
X
Z
CheckUse the other scale on the protractor to find the measure ofXYZ. 110° - 30° = 80°.
Additional Example 1 ContinuedUse a protractor to find the measure of XYZ . 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 MeasuresEstimate 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 2Estimate 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 ApplicationThe 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 ContinuedThe 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 3A 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 ContinuedA 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