Lessons 1, 2, 3 in Grade 7 Mathematics.ppt

Math 7

5. If all the s in a Δadd up to 180
o
. Then
what about the s in a quadrilateral and
pentagon?
3 * 180 = 540
o
How about a hexagon?
4 * 180 = 720
o
2 * 180 = 360
0

6. # of
sides
# of
triangles
Sum of
measures of
interior angles
3 1
1(180)=180
4 2
2(180)=360
5 3 3(180)=540
6 4 4(180)=720
n
n-2 (n-2) • 180

7. If a convex polygon has nsides,
then the sumof the measure of
the interior angles is
(n –2)(180°)

8. If a regular convex polygon
has nsides, then the measure
of oneof the interior angles isn
n180)2(

9. Ex. 1 Use a regular 15-gon to answer the questions.
A)Find the sum of the measures of the
interior angles.
B)Find the measure of ONE interior angle
2340°
156°

10. Ex: 2 Find the value of x in the polygon
130
126
143
100
117
x
126 + 130 + 117 + 143 + 100 + x = 720
616 + x = 720
x = 104

11. Ex: 3 The measure of each interior angle is 150°,
how many sides does the regular polygon have?

n
n 180)2(
One interior angle150
180)2(


n
n nn 150180)2(  nn 150360180  36030n 12n
A regular
dodecagon

12. Two more important terms
Exterior
Angles
Interior
Angles

14. The sumof
the measures
of the exterior
angles of a
convex
polygon, one
at each vertex,
is 180°.
1
2
3
4
5
1
3
2
1
3
2
4

20. Look on the
bottom of the
Worksheet