51 pts
please answer asap.

for the following diagram, assume that L || M

Solve for each of the variables, x and y. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find the solution.

y=15

x=80

Step-by-step explanation:

We know that 6y = 90  Vertical angles are equal

6y =90

Divide each side by 6

6y/6 = 90/6

y =15

The figure is a quadrilateral so the sum of the angles is 360 degrees

We will call the top left angle z

<z and the right angle are alternate interior angles and alternate interior angles are equal so  <z = 90

<z + < 6y + <x + 100 = 360

90 + 90 + <x +100 =360

Combine like terms

280 +<x = 360

Subtract 280 from each side

280-280 +<x = 360-280

x =80

6y + 90 = 180

(Supplementary angles)

6y = 90

y = 15°

Angle between line L and Q is x because of corresponding angles.

100 + x = 180

(Supplementary angles)

x = 180 - 100

x = 80°

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: