4. A kite is made by joining two congruent isosceles triangles, as shown.
What is the value of $x$ ?
A 36
B 54
C 60
D 72
E 80
4. D As $P Q=P R, \angle P R Q=\angle P Q R=x^{\circ}$. Also, as $P R=P S, \angle P R S=\angle P S R=x^{\circ}$. Therefore, $\angle Q R S=(2 x)^{\circ}$. The sum of the interior angles of quadrilateral $P Q R S$ is $360^{\circ}$. Therefore $x+x+2 x+x=360$, so $5 x=360$. Hence $x=72$.