Question

In a 5 point star, what is the sum of the measure of angles A, B, C, D, and E, if each point of the star represent each angle?

Answer 1

Look at the attached star. There is a pentagon on the inside. We are going to assume this is a regular pentagon, because it will be the same either way.

First, find the total number of degrees inside the pentagon. Next, find the measure of EACH angle of the pentagon. Find the angle that is supplementary to the angle to find the base angles of each isosceles triangle (the triangles that branch off of the pentagon).

To find the total number of degrees. We use the formula
\[180((sides)-2)\]\[180(5-2)=540^{\circ}\]

This means that each of the 5 angles has a measure 540/5, or 108 degrees.

A base angle of the isosceles triangles is supplementary to this 108 degree angle, which gives it a measure of 180-108=72 degrees.

Both base angles have the same measure. All the angles of a triangle add up to 180, so calling the angle of the pointy end of the star "x," we get
180=72+72+x
x=36 degrees.

Each point of the star has a measure of 36 degrees. There are 5 points, so 5*36=180 degrees.

Answer 2

Hell yea