   Chapter 6.4, Problem 23E 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

Quadrilateral A B C D is inscribed in circle P (not shown). If ∠ A is an acute angle, what type of angle is ∠ C ?

To determine

To find:

The type of angle is C.

Explanation

Given:

Quadrilateral ABCD which is inscribed in circle P and A is an acute angle.

Property Used:

The measure of an inscribed angle of a circle is half the measure of its intercepted arc. Consider the figure below, let the inscribed angle be 2.

Then m2=12mHJ and generally HKKJ.

Calculation:

Suppose ABCD is a quadrilateral inscribed in circle P and A is an acute angle

Since, the measure of an inscribed angle of a circle is half the measure of its intercepted arc therefore mA=12mBCD and mC=12mDAB.

But, mBCD+mDAB=360°

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