Question

The exterior angles of a regular pentagon are x°, 2x°, 3x°, 4x°, 5x°. Calculate the magnitude of each angle.

Answer 1

Step 1

The sum of exterior angles of any polygon is 360 degrees.

Step 2

x°, 2x°, 3x°, 4x°, 5x°

`\begin{gathered} x°+2x°+3x°+4x°+5x°\text{ = 360} \\ 15x\text{ = 360} \\ x\text{ = }(360)/(15) \\ x\text{ = 24} \end{gathered}`

Step 3

Each exterior angle

x°, 2x°, 3x°, 4x°, 5x°

24, 48, 72, 96 , 120

Final answer

24, 48, 72, 96 , 120