   Chapter 6.CT, Problem 7CT ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Given the tangents with m ∠ 3 = 46 ° , find:a) m R S T ⌢                                   _ b) m R T ⌢                                   _ To determine

(a)

To find:

mRST.

Explanation

Theorem used:

The measure of an angle formed when two secants intersect at a point outside the circle is one-half the difference of the measure of the two intercepts arcs.

Given:

m3=46°.

Calculation:

Consider the figure,

From the theorem we know that,

m3=mRSTmRT2(1).

Let us consider, mRST=x°.

And mRT=360°x°

Substitute for mRST and mRT in (1) we have,

To determine

(b)

To find:

mRT.

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