22. The diagram shows a regular pentagon and an irregular quadrilateral.
What is the sum of the three marked angles?
A $72^{\circ}$
B $90^{\circ}$
C $108^{\circ}$
D $126^{\circ}$
E $144^{\circ}$
22. C The exterior angle of a regular pentagon is $\frac{360^{\circ}}{5}=72^{\circ}$.
Therefore the interior angle of a regular pentagon, in degrees, is $180-72=108$. The angles at a point sum to $360^{\circ}$, so the reflex angle in the irregular quadrilateral, in degrees, is $360-108=252$. Finally the interior angles of a quadrilateral sum to $360^{\circ}$, so the sum of the marked angles, in degrees, is $360-252=108$.
(Note that the sum of the three marked angles equals the interior angle of the pentagon.)