Download Ch. 7-6 Online Notes

Name
Class
Date
Lesson 7-6
Angles and Polygons
Lesson Objective
Common Core State Standard
To find the angle measures of a polygon
Geometry: 8.G.5
Vocabulary and Key Concepts
For a polygon with n sides, the sum of the measures of the interior angles
is (n 2 2)180° .
Exterior angles are angles formed by a side and an extension of an adjacent side.
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Polygon Angle Sum
Interior angles are the angles inside a polygon at its vertices.
Common Polygons
Number of Sides
Polygon Name
Number of Sides
Triangle
3
Octagon
8
Quadrilateral
4
Nonagon
9
Pentagon
5
Decagon
10
Hexagon
6
Dodecagon
12
7
Heptagon
Example
1 Sum of the Interior Angle Measures Find the sum of the measures
of the interior angles of an octagon.
An octagon has 8 sides.
(n
2)180
(8
)
2 180° d Substitute 8 for n.
1,080
°
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Polygon Name
d Simplify.
Quick Check
1. What is the sum of the measures of the interior angles of a heptagon? 900°
72
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Course 3 Lesson 7-6
Daily Notetaking Guide
10/10/12 5:46 PM
Name
Class
Date
Examples
2 Angle Measures of a Polygon Find the missing angle measure
in the hexagon.
1478
Step 1 Find the sum of the measures of the interior angles
of a hexagon.
(n
(
2)180°
6
808
)
1208
2 180° d Substitute 6 for n.
720°
x8
d Simplify.
1368
1158
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Step 2 Write an equation.
Let x 5 the missing angle measure.
120°
720°
80°
598°
720
122°
115°
147°
136°
x
x°
x°
d Write an equation.
d Add.
d Subtract
598°
from each side.
The missing angle measure is 122° .
3 Finding the Measure of an Exterior Angle /2 is an exterior angle of ABC.
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
What is m/2 ?
m/2 5 m/A 1 m/B
B
d Exterior angle of triangle
5 37° 1 90° d Substitute.
5 127° d Simplify.
A
1
37°
C
2
/2 measures 127°.
Check
By the angle sum of a triangle, m/1 5 180° 2 90° 2 37° 5 53°.
/1 and /2 are supplementary, so m/2 5 180° 2 53° 5 127°.y
Quick Check
2. A hexagon has five angles with measures of 142°, 84°, 123°, 130°,
and 90°. What is the measure of the sixth angle?
1238
1308
848
151°
3. In RST, m/R 5 63° and m/S 5 84°. What is the measure of the
exterior angle at vertex T ?
1428
x8
147°
Daily Notetaking Guide
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Course 3 Lesson 7-6
73
10/10/12 5:46 PM