Download 7-8 Angles in Polygons

7-8 Angles in Polygons
Learn to find the measures of angles in
polygons.
Course 2
7-8 Angles
Insert Lesson
Title Here
in Polygons
Vocabulary
diagonal
Course 2
7-8 Angles in Polygons
Additional Example 1: Determining the Measure of
an Unknown Interior Angle
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
7-8 Angles in Polygons
Try This: 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
7-8 Angles in Polygons
The sum of the angle measures in other
polygons can be found by dividing the
polygon into triangles. A polygon can be
divided into triangles by drawing all of the
diagonals from one of its vertices.
Course 2
7-8 Angles in Polygons
A diagonal of a polygon is a segment that is
drawn from one vertex to another and is not one
of the sides of the polygon. You can divide a
polygon into triangles by using diagonals only if
all of the diagonals of that polygon are inside the
polygon. The sum of the angle measures in the
polygon is then found by combining the sums of
the angle measures in the triangles.
Course 2
7-8 Angles in Polygons
Number of
triangles
in pentagon
3
Course 2
Sum of angle
measures
in each
triangle
·
180°
Sum of angle
measures
in pentagon
=
540°
7-8 Angles in Polygons
Additional Example 2A: Drawing Triangles to Find
the Sum of Interior Angles
Divide each polygon into triangles to find the
sum of its angle measures.
A.
6 · 180° = 1080°
There are 6 triangles.
The sum of the angle measures
of an octagon is 1,080°.
Course 2
7-8 Angles in Polygons
Additional Example 2B: Drawing Triangles to Find
the Sum of Interior Angles
Divide each polygon into triangles to find the
sum of its angle measures.
B.
10 · 180° = 1,800°
There are 10 triangles.
The sum of the angle measures of a 12-sided
polygon is 1,800°.
Course 2
7-8 Angles in Polygons
Try This: Example 2A
Divide each polygon into triangles to find the
sum of its angle measures.
A.
4 · 180° = 720°
There are 4 triangles.
The sum of the angle measures
of a hexagon is 720°.
Course 2
7-8 Angles in Polygons
Try This: Example 2B
Divide each polygon into triangles to find the
sum of its angle measures.
B.
2 · 180° = 360°
There are 2 triangles.
The sum of the angle measures
of a square is 360°.
Course 2
7-8 Angles in Polygons
Formula for Sum of Interior Angles
The sum of interior angles
is equal to the number of
sum = 180(n – 2)o
o
sides minus 2 times 180 . where n is the number of sides
Course 2
7-8 Angles in Polygons
Formula for Sum of Interior Angles
Use the formula to find the sum of its angle
measures.
A.
sum = 180(8 – 2)°
sum = 180(6)°
There are 8 sides.
The sum of the angle measures
of an octagon is 1,080°.
Course 2
7-8 Angles in Polygons
Formula for Sum of Interior Angles
Use the formula to find the sum of its angle
measures.
B.
sum = 180(10 – 2)° There are 10 sides.
sum = 180(8)°
The sum of the angle measures
of an decagon is 1,440°.
Course 2
7-8 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 obtuse triangle with angle measures of 42°
and 32°
106°
4. Divide a seven-sided polygon into triangles to
find the sum of its interior angles *Or use the formula*
900°
Course 2
Homework
7-8 Worksheet
Study for fraction quiz Thursday
Study for 7-2 to 7-8 quiz Thursday