1 / 5

# EXAMPLE 1 - PowerPoint PPT Presentation

Find the sum of the measures of the interior angles of a convex octagon. ( n – 2) 180 ° =. ( 8 – 2) 180 °. = 6 180°. ANSWER. The sum of the measures of the interior angles of an octagon is 1080° . Find the sum of angle measures in a polygon. EXAMPLE 1. SOLUTION.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' EXAMPLE 1' - dunne

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Find the sum of the measures of the interior angles of a convex octagon.

(n – 2) 180° =

(8 – 2) 180°

= 6 180°

The sum of the measures of the interior angles of an octagon is 1080°.

Find the sum of angle measures in a polygon

EXAMPLE 1

SOLUTION

An octagon has 8 sides. Use the Polygon Interior Angles Theorem.

Substitute 8 for n.

Subtract.

= 1080°

Multiply.

( convex octagon.n–2) 180° =

900°

n–2 =

5

7

n =

The polygon has 7 sides. It is a heptagon.

Find the number of sides of a polygon

EXAMPLE 2

The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides.

SOLUTION

Use the Polygon Interior Angles Theorem to write an equation involving the number of sidesn. Then solve the equation to find the number of sides.

Polygon Interior Angles Theorem

Divide each side by 180°.

360° convex octagon.

x° + 2x° + 89° + 67° =

360

3x + 156 =

68

x =

Find the variable based on the exterior angles

EXAMPLE 3

SOLUTION

Use the Polygon Exterior Angles Theorem to write and

solve an equation.

Polygon Exterior Angles Theorem

Combine like terms.

Solve for x.

The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle and (b)the measure of each exterior angle.

a.

Use the Polygon Interior Angles Theorem to find the sum of the measures of the interior angles.

(n –2) 180° =

(12 – 2) 180° =

Find angle measures in regular polygons

EXAMPLE 4

TRAMPOLINE

SOLUTION

1800°

Since a dodecagon has 12 congruent interior angles:

1800°

Divide

= 150 °

12

The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle and (b)the measure of each exterior angle.

b.

By the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles, one angle at each vertex, is 360°.

Find angle measures in regular polygons

EXAMPLE 4

TRAMPOLINE

SOLUTION

A dodecagon has 12 exterior angles

360°

Divide

= 30 °

12