   Chapter 4.2, Problem 33E 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

For Exercises 32 to 35, consider kite A B C D with A B ¯ ≅ A D ¯ and B C ¯ ≅ D C ¯ . For kite A B C D , m ∠ C = m ∠ - 30 while m ∠ A = m ∠ B - 50 . Find m ∠ B .

To determine

To find:

mB

Explanation

Calculation:

Given,

The kite ABCD with

mC=mB-30, and

mA=mB-50.

In any quadrilateral, the sum of all the four interior angles is 360°

Thus,

A+B+C+D=360°

But, for the kite ABCD

B=D

A+B+C+B=360°

A+2B+C=360°

Now,

B-50°+2B+B-30°=360°

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