How many different rectangles can be formed by connecting four of the dots in a3x3 square such that the sides of the rectangle are parallel to the sides of the grid?

since a 3x3 square of dots forms 3 vertical and 3 horizontal lines, we need to choose 2 from 3 for both horizontal and vertical.

3! /2! * 3! /2!

3*3 = 9

9 different rectangles can be formed.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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