Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

Solution:

The sum of exterior angles of a polygon is 360°.

The measure of each exterior angle of a regular polygon with 'n' sides = 360/n

Each exterior angle of a regular decagon = 360/10 = 36

Given each exterior angle = (3x + 6)°

⇒(3x + 6)° = 36°

Solving for x, we get 3x = 30°

x = 10°

Therefore, the value of x is 10.

Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

Summary:

Each exterior angle of a regular decagon has a measure of (3x + 6)°. The value of x is 10.