Explanation:
y = 37 + x
the 4th angle (bottom right) is
360 - 90 - 90 - 125 = 55°
because the sum of all angles in any quadrilateral is 360°.
now we can assume a right-angled triangle on the right side of the trapezium.
one leg is 15 cm (like the left side), the other leg is x cm. and the right side of the trapezium is the Hypotenuse.
the bottom right angle is 55°.
the upper angle is 125 - 90 = 35°.
we can use the law of sine to get x.
the law of sine is
a/sin(A) = b/(sin(B) = c/sin(C)
with a, b, c being the sides of the triangle opposite of the corresponding angles A, B, C.
so,
15/sin(55) = x/sin(35)
x = 15×sin(35)/sin(55) = 10.50311307... cm
y = 37 + 10.50311307... = 47.50311307... ≈
≈ 47.5 cm