Question

The measures of the exterior angles of an octagon are x°x°, 2x°2x°, 3x°3x°, 4x°4x°, 5x°5x°, 6x°6x°, 9x°9x°, and 10x°10x°. Solve for xx.

Answer 1

To find x for the exterior angles of an octagon, add all the given angles expressed in terms of x, set the sum equal to 360° (the total sum of exterior angles of any polygon), and solve for x. The solution is x = 9°.

Step-by-step explanation:

The student is asking to solve for x in the context of the measures of exterior angles of an octagon. The sum of the exterior angles of any polygon is 360°. Given the exterior angles x°, 2x°, 3x°, 4x°, 5x°, 6x°, 9x°, and 10x°, we can set up an equation to find x.

Add all the exterior angles together: x + 2x + 3x + 4x + 5x + 6x + 9x + 10x.

Combine like terms to get the total sum: 40x°.

Set the equation equal to 360° (sum of exterior angles of a polygon): 40x = 360.

Solve for x by dividing both sides by 40: x = 9°.

Answer 2

x=10

Step-by-step explanation:

Given: =The exterior angles of an octagon are x°,2x°,3x°,4x°,5x°,6x°,7x°,8x°.

Then, x°+2x°+3x°+4x°+5x°+6x°+7x°+8x° =360°

⇒ 36x = 360

⇒ x= 10