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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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A polygon with four sides is called quadrilateral. Consider the figure and the dashed auxiliary line. What is the sum of the measures of the four interior angles of this (or any other) quadrilateral?

Chapter 2.4, Problem 42E, A polygon with four sides is called quadrilateral. Consider the figure and the dashed auxiliary

To determine

The sum of the measures of the four interior angles of the quadrilateral.

Explanation

Given:

A quadrilateral of side MNPQ.

Figure (1)

Properties:

The sum of the three angles in a triangle is 180°.

Calculation:

In triangle, ΔMNP

mNPM+mNMP+mN=180°(1)

In triangle, ΔMPQ

mMPQ+mPMQ+mQ=180°(2)

From the figure (1) the angle mNMQ and the mNPQ can be written as,

mNMQ=mNMP+mPMQ

mNPQ=mNPM+mMPQ

Calculate the sum of the measures of the four interior angles of the quadrilateral.

x=mNMQ+mQ+mNPQ+mN(3)

Here, the measures of the four interior angles of the quadrilateral is x

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