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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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Given: Quadrilateral RSTQ with exterior s at R and T.
Prove: m 1 + m 2 = m 3 + m 4

Chapter 2.5, Problem 27E, Given: Quadrilateral RSTQ with exterior s at R and T. Prove: m1+m2=m3+m4

To determine

To prove:

m1+m2=m3+m4

Explanation

Given:

The following figure shows the given diagram.

Figure (1)

QRS is supplementary to 1 as shown in given figure.

QTS is supplementary to 2 as shown in given figure.

Approach:

The completed proof is shown in the following table.

Proof
Statements Reasons
1. The QRS is supplementary to 1.
The QTS is supplementary to 2.
1. Given
2.m1+mQRS=180°m2+mQTS=180° 2. The sum of measures of two supplementary angles is 180°
3.m3+m4+mQRS+mQTS=360° 3. The sum of measures of four angles in a quadrilateral is,
180×(42)=360°
4.m1+m2=m3+m4 4

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