Question

3. A decagon has six equal exterior angles. Each of the

remaining four is fifteen degrees larger than these six
angles. Construct an equation and then solve it to find the
sizes of the angles.

Answer 1

30,30,30,30,30,30,45,45,45,45

Explanation:

The sum of the exterior angles is 360.

Let x = the equal one of the six equal angles

6x + 4( x + 15) = 360 Distribute the 4

6x + 4(x) + 4(15) = 360

6x + 4x + 60 = 360 subtract 60 from both sides

6x + 4x + 60 - 60 = 360 - 60

6x + 4x = 300 Combine like terms

10x = 300 Divide both sides by 10

`(10x)/(10)` =
`(300)/(10)`

x = 30

30 + 15 = 45