Question

The measures of the exterior angles of a heptagon are 3x°, 4x°, 5x°, 6x°, 8x°, 9x°, and 10x°. Find the measure of the smallest exterior angle.

Answer 1

the measure of the smallest exterior angle of the heptagon is 24 degrees.

Explanation:

The sum of the exterior angles of any polygon is always 360 degrees. Therefore, we can write an equation based on this fact and solve for x:

3x° + 4x° + 5x° + 6x° + 8x° + 9x° + 10x° = 360°

Simplifying the left side:

45x° = 360°

Dividing both sides by 45:

x° = 8°

Now we can substitute this value of x back into each of the given exterior angles to find their measures:

Smallest exterior angle: 3x° = 3(8°) = 24°

Therefore, the measure of the smallest exterior angle of the heptagon is 24 degrees.