Question

The measures of 13 of the 14 angles of a 14−gon add up to 2,004°. What must the fourteenth angle measure be?

Answer 1

156°

Explanation:

The interior angles of a convex n-gon add to (n -2)180°, so a 14-gon has a sum of angles of 12×180° = 2160°. Since 13 angles sum to 2004°, the remaining one must be ...

... 2160° -2004° = 156°