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Basic Geometry

Basic Geometry

Angles in a Polygon Examples

Example 1

What is the sum of the angles in a dodecagon?dodecagon

A dodecagon has 12 sides, so (12-2) x 180 degrees = 1800 degrees.

Example 2

What is the measure of each angle in a regular nonagon?

nonagon

A nonagon has 9 sides. Using our formula, (9-2) x 180 degrees = 1260 degrees.

Example 3

Find the missing angle.

Triangle (find missing angle)

A triangle has 180°. If we add the measures of angles I and J and subtract from 180, we get:

180 - (35 + 115) degrees

Example 4

Find the measurement of angle Q

hexagon LMNOPQ

This is a hexagon. The total number of degrees equals:
(6-2) x 180 degrees

4 x 180 degrees

720 degrees

Example 5

Find the missing angles in this isosceles trapezoid.

Isosceles Trapezoid

Since this is an isosceles trapezoid, angles I and L are congruent. In addition, angles J and K are congruent, so

m < L = m < I = 45 degrees

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