Ineed in find the value of the variables

11: x=90 and y=10

12:  x=59 and y=48

14?: x = 28,   y = 20 and z = 56

15:  x = 4 and y = 53

Step-by-step explanation:

11:  Since two sides are parallel, you can draw a transversal (a line that crosses through both) that makes sure all angles it makes are 90 degrees.  (let me know if that doesn't make sense.  Now you have two trapezoids.  One has angle measures 90+90+90+x=360 and the other has 90+90+77+y = 360.  Doing some quick algebra gets you x=90 and y=10

12:  We do the same thing, transversal throught he parallel lines to get four  90 degree angles.  Now 360 = 90 + 90 + 2x + 62 makes x = 59 and 360 = 90 + 90 +3 y + 42 makes y = 48

(14?  the one to the left of 15):  Could do the same thing to solve for x, then we need to do something different for y and z.  so first 90 + 90 + 68 + 4x = 360 so x=28.  Now, since this is an isosceles trapezoid it means the two top angles are equal and the two bottom angles are equal.  so 68 =3y+8 so y = 20 and 2z = 4x = 4(28)  makes z = 56

for 15 we'll start with y.  We will call the two equal angles a, because we need to use them.  Since the top and bottom  parts are parallel, 106 + a = 180 and 2y + a = 180.  Use a system of equations to find a = 74 and y = 53 (You just needed y of course).  since 2y=106, we know that 4x=6x-8 so then we can solve for x = 4

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: