   Chapter 2.5, Problem 46E ### 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
1 views

# For concave pentagon ABCDE, find the measure of the reflex angle at vertex E if m ∠ A = m ∠ D = x , m ∠ B = m ∠ C = 2 x , and m ∠ E = 4 x .(HINT: ∠ E is the indicated reflex angle.)

To determine

To find:

The measure of the reflex angle at vertex E.

Explanation

Given:

The following figure shows the hexagon ABCDE.

mA=mD=xmB=mC=2x

And,

mE=4x

Pentagon has 5 sides.

Formula used:

The formula to calculate the sum of interior angle of an n sided regular polygon is given by S=(n2)180°

Calculation:

Substitute 5 for n in the above mentioned formula to obtained the value of S.

S=(52)180°=3×180°=540°

Equation for sum of interior angles of pentagon is as follows,

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