   Chapter 2.5, Problem 33E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Find the measure of each (a) acute interior angle of a regular pentagram (b) reflex interior angle of the pentagram.

To determine

a)

To find:

The measure of acute interior angle of a regular pentagram.

Explanation

Given:

A pentagram (ABCDE) is a five pointed star that is shown below.

Figure (1)

Formula used:

The formula to calculate each exterior angle of an n sided regular polygon is given by,

E=360°n

Property used:

According to the theorem of triangle the sum of three angle of a triangle will be 180°.

Calculation:

Substitute 5 for n in the above mentioned formula to obtain the value of E.

E=360°5=72°

mABF=mFAB because in pentagram the triangles formed are isosceles triangle.

mFAB=72°mABF=72°

Consider the ΔABF

To determine

b)

To find:

The measure of reflex interior angle of a regular pentagram.

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