   Chapter 6.CR, Problem 6CR 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

In Review Exercises 5 to 10, B A → is tangent to the circle at point A in the figure shown. m A D C ^ = 295 ° ,     m A D ^ = 155 ° ,   m ∠ B =   ? To determine

To find: mB

Explanation

Theorem:

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

2) The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Calculation:

Given that

mADC^=295°, mAD^=155° and BA is tangent to the circle at point A.

But, mADC^+mAC^=360° since both the arcs completes the circle.

So, 295°+mAC^=360°

Subtract 295° from both the sides

295°+mAC^-295°=360°-295°

Therefore,

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