Chapter 5.2, Problem 16E

### 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 = x , m ∠ J = x + 50 , m ∠ D = x + 35 and m ∠ K = 2 x − 45 , find x .

To determine

To calculate:

The value of x.

Explanation

Given:

mâˆ A=x,â€‰â€‰mâˆ J=x+50,â€‰â€‰mâˆ K=2xâˆ’45â€‰â€‰â€‰andâ€‰â€‰mâˆ D=x+35.

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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