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Example: a regular 15-gon
The sum of the interior angles of any regular polygon of n sides is equal to 180(n - 2) degrees.
180 x 13 = 2340
There are fifteen angles.
2340/15 = 156
An interior angle of a regular 15-gon is 156 degrees.
There are two ways to find the exterior angles. The interior and exterior angles add up to 180.
180 - 156 = 24.
The exterior angles of any polygon add up to 360.
360/15 = 24
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How many sides does an equiangular polygon have if the measure of an angle of the polygon exceeds four times the measure of one of it's exterior angles by 30?
Interior angle + Exterior angle = 180 So Interior angle = 180 - Exterior angle Interior angle = 4*Exterior angle + 30 Substitute for Interior angle: 180 - Exterior angle = 4*Exterior angle + 30 Collect like terms: 150 = 5*Exterior angle Divide by 5: Exterior angle = 30 deg Therefore number of sides = 360/30 = 12
What is the measure of each interior and each exterior angle of a regular nonagon?
Each exterior angle: 40 degrees Each interior angle: 140 degrees
The measure of an exterior angle of a triangle is what equal to the measure of either remote interior angle?
never
Give the formulas for finding the number of sides of a regular polygon when given the measure of an interior angle?
180-interior angle = exterior angle 360/exterior angle = number of sides
The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle?
Very rarely.
