Chapter 4.2, Problem 42E

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

If the length of side A B ¯ (for kite A B C D ) is 6 in., find the length of A C ¯ (not shown). Recall that m ∠ A = m ∠ C = m ∠ D = 30 ° .

To determine

The length of AC¯.

Explanation

Calculation:

Given,

ABCD is a kite

mâˆ A=mâˆ C=mâˆ D=30Â°

AB=6 in.

Now, draw the line segment ACÂ¯.

In a kite the sum of all the interior angles is 360Â°.

Thus,

âˆ A+âˆ B+âˆ C+âˆ D=360Â°

30Â°+âˆ B+30Â°+30Â°=360Â°

âˆ B+90Â°=360Â°

âˆ B=360Â°-90Â°

âˆ B=270Â°

Therefore, the indicated reflex angle is 270Â°.

Thus, in âˆ†ABC âˆ B is given by

âˆ B=360Â°-270Â°

âˆ B=90Â°

Also, in a kite that the pairs of adjacent sides are equal in length

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