Question

The measures of 6 of the interior angles of a heptagon are: 120°, 150°, 135°, 170°, 90°, and 125°. What is the measure of the largest exterior angle?

Answer 1

1. consider one angle of a (convex) heptagon. From that angle you can construct 7-3=4 diagonals. (-3 because we cannot create diagonals with the adjacent vertices and the angle itself )

2. 4 diagonals create 5 triangular regions. (check the picture)

3. So the sum of the measures of the interior angles of the heptagon is 180°*5=900°.

4. The measure of the remaining 7th interior angle is 900°-(120+150+135+170+90+125)°=110°.

5. The largest exterior angle is when the interior angle is the smallest.

6. The smallest interior angle is 90°, so the largest exterior angle is 180°-90°=90°


Answer: 90°