7. Five line segments are drawn inside a rectangle as shown. What is the sum of the six marked angles?
A $360^{\circ}$
B $720^{\circ}$
C $900^{\circ}$
D $1080^{\circ}$
E $1120^{\circ}$
Solution
D

The six marked angles, together with the 4 right angles of the rectangle, are the 10 interior angles of a decagon. Since angles in a decagon add up to $(10-2) \times 180^{\circ}=8 \times 180^{\circ}$, the six marked angles add up to $(8 \times 180-4 \times 90)^{\circ}=6 \times 180^{\circ}=1080^{\circ}$.