Question

please help with question #10. the teacher said to solve it using systems of equations. and we are required to show all of our work. I hope you can figure this out, thanks!!

Answer 1

x = 20 and y = 25

Step-by-step explanation

We are given three angles

We have that:

From the figure, we see that

This means that they are equal to one another.

That is:

=> 3x + 2 = 4x - 18

Collect like terms:

4x - 3x = 2 + 18

x = 20

We also see that

Adjacent angles of a parallelogram add up to 180 degrees.

This means that:

5y - 7 + 4x - 18 = 180

Recall that x = 20:

5y - 7 + 4(20) - 18 = 180

5y - 7 + 80 - 18 = 180

5y + 55 = 180

5y = 180 - 55 = 125

=> y = 125 / 5

y = 25

Therefore, x = 20 and y = 25.