Respuesta :

MrGumby

The answer is that x = 5 and y = 4.

Since we are given congruence on these sides, we can set the amounts equal to each other. We'll start with those labelled with two lines.

7x - 4 = 31 ---> add 4 to both sides

7x = 35 ----> divide by 7 on both sides

x = 5

Now we can do the same for the three line side

4y + 8 = 24 ---> subtract 8 from both sides

4y = 16 ---> divide both sides by 4

y = 4

The lines on the sides represent the two sides are equal.

Hence, the side, AC=PR, the sides with one line each.

The sides, AB=PQ, the sides with two line each.

The sides, BC= QR, the sides with three line each.

Hence, By SSS congurency the two triangles are congurent.

As the two triangles are congurent.

And, The sides are equal

AB=PQ

So, 7x-4=31

Adding 4 on both sides

7x-4+4=31+4

7x=35

To solve for x, Divide by 7 on both sides

x=35/7

x=5

Also, BC=QR

So,4y+8=24

Subtracting 8 from both sides

4y+8-8=24-8

4y+0=16

4y=16

To solve for y, Let us divide by 4 on both sides

4y/4=16/4

y=4

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