Question

Given that ABCD is an isosceles trapezoid, find x and y.

Answer 1

Answer:
x = 15
y = 40

Explanation:
1- getting the value of x:
We are given that the two sides (x-4) and (11) are equal. This means that:
x - 4 = 11
x = 11 + 4 
x = 15
2- getting the value of y:
For any polygon, the sum of measures of its angles is equal to (n-2)*180 where n is the number of sides.
The given is a trapezoid, therefore, it has n - 4
sum of its interior angles = (4-2)*180 = 360
We are given that each two opposite angles are equal.
Therefore:
360 = 2 (4y - 20) + 2y
360/2 = 4y - 20 + y
180 = 5y - 28
200 = 5y
y = 200/5
y = 40

Hope this helps :)

Answer 2

X = 15

Y= 34

11 + 4 = 15

360 = 2(4y-20) + 2y
360 = 10y -20
340 = 10y
34 = y