Download 7-8 Angles in Polygons

7-8 Angles in Polygons
Problem of the Day
How many different rectangles are in the
figure shown? 100
Course 2
7.8 Angles in Polygons
Objective:
Learn to find the measures of angles in
polygons.
7-8 Angles
Insert Lesson
Title Here
in Polygons
Vocabulary
diagonal
Course 2
PROVE IT!
The sum of all
angles in a
triangle add up
to 180 degrees…
How could you
prove this
theory???
Take your triangle
and prove why
the 3 angles
have a sum of
180°.
7-8 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
7-8 Angles in Polygons
You can prove mathematically that the angle
measures in a triangle add up 180° by drawing
a diagram using the following steps.
a. Draw a triangle.
b. Extend the sides
of the triangle.
c. Draw a line through the vertex
opposite the base, so that the
line is parallel to the base.
Course 2
7-8 Angles in Polygons
1
4
2
3
5
1, 2, and 3 together form a straight angle.
Notice that
That is, the sum of their measures is 180°.
Notice also that the figure you have drawn consists of two
parallel lines cut by two transversals. So if you were to tear off
4 and 5 from the triangle, they would fit exactly
over 1 and 3. This shows that the sum of the measures
of the angles in the triangle are 180°.
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°
x=
Subtract 120° from both sides.
60°
The measure of the unknown angle is 60°.
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.
Course 2
On the orange lab sheet, draw in as
many diagonals as you can
WITHOUT crossing the diagonals.
The diagonals must be drawn from
vertex to vertex.
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
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
Fill out the chart:
Shape
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
# of
sides
# of
# of
degrees
angles triangles
Shape
# of
sides
# of
angles
# of
degrees
triangles
Triangle
3
3
1
180°
Quadrilateral
4
4
2
360°
Pentagon
5
5
3
540°
Hexagon
6
6
4
720°
Heptagon
7
7
5
900°
Octagon
8
8
6
1080°
Nonagon
9
9
7
1260°
Decagon
10
10
8
1440°
What is the rule??
The number of sides, minus 2, times 180 equals
the degrees in a polygon.
( S – 2 ) (180) = degrees in a polygon
Try these:
How many degrees does a 12 sided polygon
have? 1,800
How many degrees does a 15 sided polygon
have? 2,340
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. How many degrees does a heptagon have?
900°
Course 2