Chapter 5.2, Problem 15E

### 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

# Quadrilateral A B C D ∼ quadrilateral H J K L . If m ∠ A = 55 ∘ , m ∠ J = 128 ∘ and m ∠ D = 98 ∘ , find m ∠ K .

To determine

To calculate:

The value of mK.

Explanation

Given:

mâˆ A=55âˆ˜,â€‰â€‰mâˆ J=128âˆ˜â€‰â€‰â€‰andâ€‰â€‰mâˆ D=98âˆ˜.

Definition Used:

The sum of measure of angle in a quadrilateral is 360âˆ˜.

Similarity between Two polygons:

Two polygons are similar if and only if when all pairs of corresponding angles are congruent and all pairs of corresponding sides are proportional.

Calculation:

According to the definition of similar polygon, âˆ Aâ†”âˆ H,â€‰â€‰âˆ Bâ†”âˆ J,â€‰â€‰âˆ Dâ†”âˆ L,â€‰â€‰â€‰andâ€‰â€‰âˆ Câ†”âˆ K

Here, congruent angles are of same measure.

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