17. The diagram shows a square, an equilateral triangle and a regular pentagon. What is the size of $\angle W U V$ ?
A $21^{\circ}$
B $23^{\circ}$
C $25^{\circ}$
D $27^{\circ}$
E $29^{\circ}$
17. A The interior angles of an equilateral triangle, a square and a regular pentagon are $180^{\circ} \div 3=60^{\circ}$, $2 \times 180^{\circ} \div 4=90^{\circ}$ and $3 \times 180^{\circ} \div 5=108^{\circ}$ respectively. Therefore the size of the obtuse $\angle U V W$ is $108^{\circ}+90^{\circ}-60^{\circ}=138^{\circ}$. Since the pentagon and the square share a side and the square and the equilateral triangle also share a side, the side-length of the pentagon is equal to the side-length of the equilateral triangle. Therefore $U V=V W$ and hence the triangle $U V W$ is isosceles and $\angle V W U=\angle W U V$. Therefore the size of $\angle W U V$ is $\left(180^{\circ}-138^{\circ}\right) \div 2=21^{\circ}$.