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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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For the concave quadrilateral ABCD, explain why the sum of the measures of the interior angles is 360 ° . (HINT: Draw B D ¯ .)

Chapter 2.5, Problem 40E, For the concave quadrilateral ABCD, explain why the sum of the measures of the interior angles is

To determine

To explain:

The reason that the Sum of the measure of the interior angles is 360°.

Explanation

Given:

The following figure shows the given diagram.

Figure (1)

Approach:

Draw an auxiliary segment BD¯ and mentioned the angles as shown below.

Figure (2)

Calculation:

By angle addition postulate,

mABC=(m1+m3)mADC=(m2+m4)

According to the angle sum property of triangle the sum of three angles in a triangle will be 180°.

In ΔBCD,

mC+m3+m4=180°

In ΔBAD,

mA+m1+m2=180°

The equation for sum of interior angles of the quadrilateral ABCD is,

S=mC+m<

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