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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In pentagon ABCDE with B D E , find the measure of interior angle D.

Chapter 2.5, Problem 4E, In pentagon ABCDE with BDE, find the measure of interior angle D.

To determine

The measure of interior angle D.

Explanation

Given:

A pentagon ABCDE with BDE.

Figure (1)

Formula used:

Write the equation to calculate the sum of the measures of the interior angles of a polygon.

S=(n2)×180°.

Here, S is the sum of the measures of interior angles of a polygon and n is sides of the polygon.

Definition:

If the angles of a pentagon are congruent, then the measures of the angles are same.

B=D=E.

Calculation:

Calculate the sum of the measures of interior angles of a polygon.

Substitute 5 for n in the above mention equation to find the sum of the measures of interior angles.

S=(52)×180°=3×180°=540°

From the figure, the sum of interior angles of pentagon is,

mA+mB+mC+mD+mE=540°.

Since, the angles of the pentagon are congruent then,

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