Download Lesson 14

Lesson 14
Measure of the Angles of Polygons
Get the idea
• The sum of the measure of interior angles of
any triangle is 180°.
• We can use this fact to help us figure out how
many degrees are inside polygons.
Example 1
• In Triangle ABC, angles A and C are congruent.
What is the measure of <A.
A
B
C
• Use what you know about the sum of the
measures of the angles in a triangle.
• x+90+x=180. So what does angle A equal?
Dividing up polygons
• Any polygon can be divided into triangles by
drawing diagonals from the same vertex. For
example, a pentagon can be divided into 3
triangles.
• We know that the sum of the measures of the
angles in each triangle in 180°. So, the sum of the
measures of the angles in a pentagon is:
180x3=540°.
Measure of Interior Angles
• You can also use the following formula to find
the total number of degrees in any polygon:
180(n-2) where n represents the number of
sides.
Example 2
• What is the measure of each interior angle in a
regular hexagon?
• There are 4 triangles. Multiply 180° by the
number of triangles. 180°x4= 720°
• There are 6 angles in a hexagon. So, 720°/6=
120°.
• The measure of each interior angle of a regular
hexagon is 120°.
How do I find each angle?
• Another way to find the measure of each
interior angle of a regular polygon is to use a
formula…
• 180(n-2), where n represent number of sides.
n
Tessellations
• A tessellation is a pattern of repeating figures in
which there are no gaps between the figures.
• A regular polygon can be used to create a
tessellation IF the measure of each interior angle
evenly divides 360°.
• If the measure of the angle does not divide into
360°, there will be gaps in the shapes when you
put them together.
• What is an example of a tessellation in everyday
life?
An example
• What shape is tessellating?
360°
Example
• Randy wants to create a tessellation using
only regular octagons. Is that possible?
– Use the formula 180(n-2) .
n
– Find the measure of each angle.
– Does it divide into 360°?
– Does it tessellate?
Practice time
• Complete pg 92 and 93 in the Coach book in
groups.
• We will complete the open-ended together.