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

• The sum of the eight interior angles not adjacent to these exterior angles is 1280°.

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Given

• A 15-sided polygon with sum of 7 exterior angles 200°.

To find

• The sum of the 8 interior angles, remote to known 7 angles.

Solution

We know that:

• sum of all exterior angles of a polygon is 360°.
• sum of each interior and exterior angle pair is 180°.

So the sum of the 8 exterior angles is:

• 360° - 200° = 160°

Sum of both interior and exterior angles of 8 angles:

• 180°×8 = 1440°

Sum of those 8 interior angles is:

• 1440° - 160° = 1280°