x = 90

The two angles marked

y^{\circ}

are equal because they are in an isosceles triangle. For the same reason, the angles

z^{\circ}

are equal. Since an exterior angle of a triangle is the same of the two interior and opposite angles, it follows that

a = 2 y

and

b = 2 z

Now $a^{\circ} + b^{\circ} = 180^{\circ}$ since they are the base angles of a parallelogram. So $2 y + 2 z = 180$ giving $y + z = 90$ . But, from the angle sum of a triangle, $x + y + z = 180$ , hence $x = 90$ .