Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

Given: Quadrilateral RSTQ with exterior ∠ s at R and T.

Prove: m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4

To determine

To prove:

m∠1+m∠2=m∠3+m∠4

The following figure shows the given diagram.

∠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.m∠1+m∠QRS=180°m∠2+m∠QTS=180°	2. The sum of measures of two supplementary angles is 180°
3.m∠3+m∠4+m∠QRS+m∠QTS=360°	3. The sum of measures of four angles in a quadrilateral is, 180×(4−2)=360°
4.m∠1+m∠2=m∠3+m∠4	4

Check out a sample textbook solution.

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

MathGeometryElementary Geometry for College Students6th Edition

Elementary Geometry for College St...

Solutions

Elementary Geometry for College St...

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

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Given: Quadrilateral RSTQ with exterior ∠ s at R and T.

Prove: m ∠ 1 + m ∠ 2 = m ∠ 3 + m ∠ 4