In an isosceles trapezoid, the non-parallel sides are congruent, and the base angles are congruent. Since the non-parallel sides are congruent, we can say that:
x = y + 20
Since the base angles are congruent, we can set up an equation using the given angle measures:
(8y + 64) + (3x) = 180 (since the sum of the angles on a straight line is 180 degrees)
Now, we can substitute the first equation into the second equation:
(8y + 64) + 3(y + 20) = 180
Expanding and simplifying the equation:
8y + 64 + 3y + 60 = 180 11y + 124 = 180
Subtracting 124 from both sides:
11y = 56
Dividing by 11:
y = 56 / 11 y = 5.09 (rounded to two decimal places)
Now, we can find x using the first equation:
x = y + 20 x = 5.09 + 20 x = 25.09 (rounded to two decimal places)
So, x is approximately 25.09, and y is approximately 5.09.
