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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

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 E A D = 70 ° ,   m B = 30 ° ,     m A C ^ = ?

To determine

To find: mAC^

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

mEAD=70°, mB=30° and BA is tangent to the circle at point A.

But, using linear pair definition mEAD+mBAD=180°

So, 70°+mBAD=180°

Subtract 70° from both the sides

70°+mBAD-70°=180°-70°

Therefore, mBAD=110°

In ADC, by angle-sum property BAD+ADB+ABD=180°

110°+ADB+30°=<

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