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8-8 Angles in Polygons
Warm Up
Problem of the Day
Lesson Presentation
Course 2
8-8 Angles in Polygons
Warm Up
Solve.
1. 72 + 18 + x = 180
x = 90
2. 80 + 70 + x = 180
x = 30
3. x + 42 + 90 = 180
x = 48
4. 120 + x + 32 = 180
x = 28
Course 2
8-8 Angles in Polygons
Problem of the Day
How many different rectangles are in the
figure shown? 100
Course 2
8-8 Angles in Polygons
Learn to find the measures of angles in
polygons.
Course 2
8-8 Angles in Polygons
If you tear off the corners of a triangle and put
them together, you will find that they form a
straight angle. This suggests that the sum of the
measures of the angles in a triangle is 180°.
Course 2
8-8 Angles in Polygons
Angles of a Triangle
The sum of the
measures of the
angles in a triangle
is 180°.
Course 2
2
1
3
m1 + m2 + m3 = 180°
8-8 Angles in Polygons
Additional Example 1: Finding an Angle Measure of
in a Triangle
Find the measure of the
unknown angle.
55°
80°
x
80° + 55° + x = 180° The sum of the measures
of the angles is 180°.
135° + x = 180° Combine like terms.
–135°
–135° Subtract 135° from both sides.
x = 45°
The measure of the unknown angle is 45°.
Course 2
8-8 Angles in Polygons
Check It Out: Example 1
Find the measure of the
unknown angle.
30°
90°
x
90° + 30° + x = 180° The sum of the measures
of the angles is 180°.
120° + x = 180° Combine like terms.
–120°
–120° Subtract 120° from both sides.
x = 60°
The measure of the unknown angle is 60°.
Course 2
8-8 Angles in Polygons
Angles of a Quadrilateral
The sum of the
measures of the
angles in a
quadrilateral is
360°.
2
3
1
4
m1 + m2 + m3 + m4
= 360°
Course 2
8-8 Angles in Polygons
Additional Example 2: Finding an Angle Measure of
in a Quadrilateral
89°
Find the unknown angle
measure in the
quadrilateral.
82°
65°
65° + 89° + 82° + x = 360°
236° + x = 360°
–236°
–236°
x = 124°
The sum of the measures
of the angles is 360°.
Combine like terms.
Subtract 236° from
both sides.
The measure of the unknown angle is 124°.
Course 2
x
8-8 Angles in Polygons
Check It Out: Example 2
92°
Find the unknown angle
measure in the
quadrilateral.
67° + 92° + 89° + x = 360°
248° + x = 360°
–248°
–248°
x = 112°
67°
x
The sum of the measures
of the angles is 360°.
Combine like terms.
Subtract 248° from
both sides.
The measure of the unknown angle is 112°.
Course 2
89°
8-8 Angles in Polygons
Additional Example 3: Drawing Triangles to Find the
Sum of Interior Angles
Divide each polygon into triangles to find the
sum of its angle measures.
6 · 180° = 1080°
There are 6 triangles.
The sum of the angle measures
of an octagon is 1,080°.
Course 2
8-8 Angles in Polygons
Check It Out: Example 3
Divide each polygon into triangles to find the
sum of its angle measures.
4 · 180° = 720°
There are 4 triangles.
The sum of the angle measures
of a hexagon is 720°.
Course 2
8-8 Angles
Insert Lesson
in Polygons
Title Here
Lesson Quiz
Find the measure of the unknown angle for
each of the following.
1. a triangle with angle measures of 66° and 77°
37°
2. a right triangle with one angle measure of 36°
54°
3. an quadrilateral with angle measures of 144°,
84°, and 48°.
84°
4. Divide a six-sided polygon into triangles to
find the sum of its interior angles
720°
Course 2