4. The diagram shows a regular pentagon inside a square.
What is the value of $x$ ?
A 48
B 51
C 54
D 60
E 72
4. C The sum of the exterior angles of a convex polygon equals $360^{\circ}$. The angle marked $p^{\circ}$ is the exterior angle of a regular pentagon. So $p=360 \div 5=72$. The angle sum of a triangle equals $180^{\circ}$, so $q=180-90-72=18$. The angle marked $r^{\circ}$ is the interior angle of a regular pentagon, so $r=180-72=108$. The angles marked $q^{\circ}, r^{\circ}$ and $x^{\circ}$ lie along a straight line, so $x=180-(q+r)$ $=180-(18+108)=54$.