Download Lesson 5 – Angles in Polygons ALP

MPM1D
Ms. Kueh
Angle Relationships in Polygons
Polygon:
Convex Polygon
Concave Polygon
Fill in the chart below from the two previous lessons. Complete questions #1 and 2, and fill in
the information as you work on the questions.
Polygon
# of sides
# of Diagonals
from one vertex
# of
triangles in
the polygon
Sum on the
interior
angles
Sum on the
exterior
angles
1. Triangle
2. Quadrilateral
3. Pentagon
4. Hexagon
For the shapes below, measure all the interior and exterior angles with a protractor. And then
calculate the sum of the interior and exterior angles:
1. Pentagon
2. Hexagon
Summary:

The sum of the exterior angles of any polygon is ______________ .

For a polygon with n-sides, the sum of the interior angles, in degrees is __________ .
 A_______________ polygon is a polygon where all the ____________ and
____________ are equal.

Shape:
Sum of the interior angles:
Triangle
Quadrilateral
Pentagon
Octagon
Example 1
Determine the sum of the interior angles in a polygon with 15 sides. Show your work.
Example 2
Determine the number of sides in a polygon if the sum of the interior angles is 5400°. Show
your work.
Example 3
A Canadian $1 coin, known as a loonie, is a regular polygon with 11 sides, called an undecagon.
Determine the sum of the interior angles of the loonie. What is the measure of one of the
interior angles?
Day 2
Draw and label an example of each shape or explain why it is not possible.
a) A triangle with one acute exterior angle.
b) A triangle with two right angles.
c) A quadrilateral with four equal angles.
d) A quadrilateral with three obtuse angles.
e) A pentagon with two obtuse angles and three acute angles
f) A convex hexagon with five acute angles.
Homework:
Day 1 pg. 391 #1-10, 16, 17
Day 2 pg. 392 #11-15, 18-21