MPM1D Angle Relationships in PolygonsMs. Kueh

Polygon –

Regular polygon –

Fill in the chart below.

# of Sides

Name of Regular Polygon

Diagram of Polygon

# of Triangles from one

vertex

Sum of Interior Angles

Each interior angle

Each exterior

angle

Sum of exterior angles

3 Triangle 1

4 Square

5 Pentagon

3 triangles

3 (180 ° )=540 °108 ° 72 ° 360 °

6 Hexagon

7 Heptagon

12 Dodecagon

20 Icosagon

n n – gon

Draw an example of a:Convex Polygon Concave Polygon

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 3A 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?

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.

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.

EQAO Angle Review:

Find x and y .

Find x and y .

Homework: pg. 391 #1-9 TIPS practice #20, 21