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