The value of the variable x obtained from the diagram is x = 13, and y = 11
The steps used to find the value of the variable is presented as follows;
The parallel sides in the figure indicates that we get;
Alternate interior angles are congruent
4·x = 52°
x = 52/4
x = 13
The interior angles in the right triangle indicates that we get;
(3·y + 5)° + 4·x° + 90° = 180° (Angle sum property of a triangle)
4·x + 3·y + 95 = 180
Plugging in the value of x obtained from above alternate interior angles indicates that we get;
4 × 13 + 3·y + 95 = 180
52 + 3·y + 95 = 180
3·y + 147 = 180
3·y = 180 - 147
y = (180 - 147)/3
y = 11