Question

The measures of the exterior angles of an octagon are x, °x°, 2, x, °2x°, 4, x, °4x°, 5, x, °5x°, 6, x, °6x°, 8, x, °8x°, 9, x, °9x°, and 10, x, °10x°. find the measure of the largest exterior angle. a) 45 degrees

b) 60 degrees
c) 75 degrees
d) 90 degrees

Answer 1

The sum of exterior angles of an octagon is 360 degrees. After finding x to be 8 degrees, it turns out that the largest exterior angle of the octagon would be 80 degrees, which is not listed in the given options.

Step-by-step explanation:

The sum of the exterior angles of any polygon is 360 degrees. Each exterior angle of the octagon is given as a multiple of x. To find x, we set up an equation based on the sum of the exterior angles:

x + 2x + 4x + 5x + 6x + 8x + 9x + 10x = 360

Add up the coefficients: 1 + 2 + 4 + 5 + 6 + 8 + 9 + 10 = 45

Therefore, 45x = 360 degree.

Now we solve for x: x = 8 degrees.

The largest exterior angle is 10x, which is 10 * 8 degrees = 80 degrees. The correct answer is not listed in the options given.