Question

A polygon has 15 sides.

(b) If the sum of seven of the exterior angles is 200°, find the sum of the
eight interior angles not adjacent to these exterior angles.

Answer 1

(a) correct

(b) The exterior angles of a polygon add to 360°, so the other 8 interior angles add to 160°. Since an exterior angle and its corresponding interior angle add to 180°, the 8 exterior-interior angle pairs we must consider add to 1440°. Thus, the answer is 1280°.