Solving for Angles in a Polygon

Polygons and Angles I

Right Angles, Acute Angles, and Obtuse Angles

- Right angles measure 90 degrees

- Acute angles measure less than 90 degrees

- Obtuse angles measure more than 90 degrees

Multiple Choice

Quick Check:

Find the value of the variable:

• 65º

• 70º

• 76º

• 56º

Multiple Choice

Quick Check:

Find the value of the variable:

• x = 15

• x = 16

• x = 14

• x = 13

Multiple Choice

Quick Check:

Find the value of the variable:

• x = 31

• x = 30

• x = 35

• x = 29

Polygons

In geometry, a polygon is a plane figure that is described by a finite number of straight-line segments connected to form a solid plane region.

Names of Polygons

• A 3-sided polygon is called a TRIANGLE

• A 4-sided polygon is called a QUADRILATERAL

• A 5-sided polygon is called a PENTAGON

• A 6-sided polygon is called a HEXAGON

• A 8-sided polygon is called a OCTAGON

• A 9-sided polygon is called a NONAGON

• A 10-sided polygon is called a DECAGON

Multiple Choice

Go ahead and try it with the triangle, What is the sum of the measures of the interior angles?

• 180º

• 360º

• 90º

• 45º

Multiple Choice

What is the sum of the measures of the interior angles of A 12-sided polygon?

• 1800º

• 1220º

• 1400º

• 1540º

Multiple Choice

What is the sum of the measures of the interior angles of An 8-sided polygon is called an OCTAGON?

• 1080º

• 1100º

• 1440º

• 1540º

Multiple Choice

What is the sum of the measures of the interior angles of A 6-sided polygon is called a HEXAGON?

• 1080º

• 720º

• 1440º

• 1540º

Multiple Choice

For a regular NONAGON, find the sun of measures of the interior angles.

• 1260º

• 1620º

• 1350º

• 1435º

Find the Measure of One Interior Angle

Interior angles of regular polygons

Find the sum of interior angles using the formula 180n-360 as before. Then divide by the number of sides to find the value of one angle.

Multiple Choice

Find the size of one interior angle of this regular hexagon

• 120º

• 125º

• 130º

• 135º

Multiple Choice

Find the size of one interior angle of this regular decagon

• 144º

• 154º

• 146º

• 139º

Multiple Choice

For a regular NONAGON, find the measure of one interior angle.

• 140

• 160

• 180

• 120

Multiple Choice

What is the value of angle aº?

• 116º

• 110º

• 120º

• 125º

Multiple Choice

What is the value of angle aº?

• 112º

• 115º

• 120º

• 125º