Chapter 12.5, Problem 42E

### Elementary Technical Mathematics

12th Edition
Dale Ewen
ISBN: 9781337630580

Chapter
Section

### Elementary Technical Mathematics

12th Edition
Dale Ewen
ISBN: 9781337630580
Textbook Problem

# Exercises 41–44 refer to Illustration 16. A B ↔ and A C ↔ are secants; C D ¯ and B F ¯ are chords.ILLUSTRATION 16Suppose B C ⌢ = 100 ° and D F ⌢ = 40 ° . Find the measure of ∠ B A C .

To determine

To calculate: The measure of BAC given that BC=100° and DF=40°, where AB and AC are secants; CD¯ and BF¯ are chords.

Explanation

Given Information:

A circle in which BCâŒ¢=100Â° and DFâŒ¢=40Â°, ABâ†” and ACâ†” are secants; CDÂ¯ and BFÂ¯ are chords.

Formula used:

The measure of an inscribed angle in a circle is equal to one-half the measure of its intercepted arc.

The exterior angle of a triangle is equal to the sum of interior opposite angles.

Calculation:

Consider the figure,

Here, BCâŒ¢ is the intercepted arc of âˆ BDC and âˆ BDC is an inscribed angle.

Similarly, DFâŒ¢ is the intercepted arc of âˆ DCF and âˆ DCF is an inscribed angle.

Further, the measure of an inscribed angle in a circle is equal to one-half the measure of its intercepted arc.

So, the measure of âˆ BDC is equal to one-half the measure of BCâŒ¢ and the measure of âˆ DCF is equal to one-half the measure of the arc given by DFâŒ¢

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