Question

The measures of the exterior angles of a pentagon are x°, 3x°, °4x°,°6x°, and °10x°. Find the measure of the largest exterior angle.

Answer 1

The sum of the exterior angles of any polygon is always 360 degrees. We can use this fact to solve for x, and then find the measure of the largest exterior angle.

The sum of the exterior angles of a pentagon is:

x + 3x + 4x + 6x + 10x = 360

Simplifying and solving for x:

24x = 360

x = 15

Now we can substitute x = 15 into each exterior angle expression to find their measures:

x° = 15°

3x° = 45°

4x° = 60°

6x° = 90°

10x° = 150°

So, the largest exterior angle has a measure of 150 degrees.