Weekly Problem 27 - 2013
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 $x =90$.