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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.4, Problem 23E
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Elementary Geometry for College St...

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

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Problem 1E
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Problem 41E
Problem 42E
Problem 43E
Problem 44E
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Problem 46E
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Chapter 1.4, Problem 23E, Exercises 1624 Given: STbisectsRSV mRST=x+y mTSV=2x2y mRSV=64 Find: xandy

Exercises 16 − 24

Given: S T →   bisects  ∠ R S V
m ∠ R S T = x + y
m ∠ T S V = 2 x − 2 y
m ∠ R S V = 64 °
Find: x     and  y

To determine

To find:

The value of x and y for given information.

Explanation

Given:

ST→ bisects ∠RSVm∠RST=x+ym∠TSV=2x−2ym∠RSV=64°

The given figure is,

Definition:

Angle addition postulate says that,

If a point say M lies in the interior of ∠PQR, then m∠PQM+m∠RQM=m∠PQR.

Calculation:

Consider the figure,

T is the interior point of the angle ∠RSV.

m∠RST=x+ym∠TSV=2x−2ym∠RSV=64°

Use above mentioned angle addition postulate to solve for the value of x.

m∠RST+m∠TSV=m∠RSVx+y+2x−2y=64

Simplify above equation,

3x−y=64…(1)

It is given that ST→ is the bisector of ∠RSV

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