SOLUTION: Consider a regular pentagon. Find the measures of the following in degrees. (a) each interior angle of a regular pentagon ° (b) each exterior angle of a regular pentagon �

Question 1191964: Consider a regular pentagon. Find the measures of the following in degrees.
(a)
each interior angle of a regular pentagon
°
(b)
each exterior angle of a regular pentagon
°
Consider extending the sides of the regular pentagon to create a regular pentagram. Find the measures of the following in degrees.
(a)
each acute interior angle of a regular pentagram
°
(b)
each reflex interior angle of a regular pentagram
°
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

The sum of the measures of the interior angles of ANY

-gon is

180° .

The measure of an interior angle of a regular

-gon is the sum of the measures of the interior angles divided by

.

The sum of measures of the exterior angles of ANY polygon is 360°.

The measure of each external angle of a regular

-gon is the sum of the measures of the external angles divided by

.

Each point of a regular pentagram is an isosceles triangle, the base angles of which are supplementary to the interior angles of the central pentagon which you calculated above. 180° minus the sum of the two base angles gives you the measure of the acute vertex angle.

The measure of the reflex angles of a regular pentagram is 180° plus the sum of two base angles from the isosceles triangle that forms one of the points of the pentagram.

You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it

From
I > Ø

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