   Chapter 6.1, Problem 12E 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: m ∠ D O E = 76 ∘ and m ∠ E O G = 82 ∘ in ⊙ O E F ¯  is a diameter Find: a) m D E ⌢ b) m D F ⌢ c) m ∠ F d) m ∠ D G E e) m ∠ E H G f) Whether m ∠ E H G = 1 2 ( m E G ⌢ + m D F ⌢ )

To determine

(a)

To calculate:

The mDE by using the provided figure.

Explanation

Given:

mDOE=76o and mEOG=82o in Q. EF¯ is a diameter.

Postulate used:

Central angle postulate:

In a circle, the degree of a central angle is equal to the degree measure of its intercepted arc.

Calculation:

Since, mDOE=76o

To determine

(b)

To calculate:

The mDF by using the provided figure.

To determine

(c)

To calculate: The F by using the provided figure.

To determine

(d)

To calculate:

The mDGE by using the provided figure.

To determine

(e)

To calculate:

The mEHG by using the provided figure.

To determine

(f)

To calculate:

The mEHG=12(mEG+mDF) by using the provided figure.

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