Chapter 6.4, Problem 24E

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7th Edition

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ISBN: 9781337614085

Textbook Problem

Quadrilateral

To determine

**To find:**

The type of quadrilateral is

Explanation

**Given:**

Quadrilateral

**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

Then

If two lines are cut by a transversal and the same side interior angles are supplementary, then the lines are parallel.

A trapezoid is a special quadrilateral that has only one pair of parallel sides. An isosceles trapezoid has one pair of parallel sides and the base angles are congruent.

**Calculation:**

Suppose

Since, the measure of an inscribed angle of a circle is half the measure of its intercepted arc therefore,

Calculating the sum of interior angles on the same side

Also,

Also, in a circle,

Since,

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