   Chapter 6.2, Problem 7E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given: In ⊙ Q , P R ¯ contains Q, M R ¯ is a tangent, m M P ⌢ = 112 ° , m M N ⌢ = 60 ° and m M T ⌢ = 46 ° Find: a) m ∠ M R P b) m ∠ 1 c) m ∠ 2 To determine

(a)

To find:

mMRP when Q, PR¯ contains Q, MR¯ is a tangent, mMP=112°, mMN=60° and mMT=46°.

Explanation

Theorem:

The measure of an angle formed by a tangent and a secant that intersect at a point outside the circle is one-half the difference of the measures of the two intercepted arc.

Calculation:

mMRP when Q, PR¯ contains Q, MR¯ is a tangent, mMP=112°, mMN=60° and mMT=46°

mMP+mMT+mTV=180°112°+46°+mTV=180°158°+mTV=180°m

To determine

(b)

To find:

m1 when Q, PR¯ contains Q, MR¯ is a tangent, mMP=112°, mMN=60° and mMT=46°.

To determine

(c)

To find:

m2 when Q, PR¯ contains Q, MR¯ is a tangent, mMP=112°, mMN=60° and mMT=46°.

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