each exterior angle of a regular decagon has a measure of (3x + 6)°. what is the value of x?\no x = 8\no x =…
each exterior angle of a regular decagon has a measure of (3x + 6)°. what is the value of x?\no x = 8\no x = 10\no x = 13\no x = 18
Answer
Explanation:
Step1: Recall exterior - angle sum property
The sum of exterior angles of any polygon is $360^{\circ}$. A decagon has 10 sides. For a regular decagon, all exterior angles are equal.
Step2: Set up the equation
If each exterior angle of a regular decagon is $(3x + 6)^{\circ}$, then $10(3x + 6)=360$.
Step3: Expand the left - hand side
$30x+60 = 360$.
Step4: Isolate the variable term
Subtract 60 from both sides: $30x=360 - 60$, so $30x = 300$.
Step5: Solve for x
Divide both sides by 30: $x=\frac{300}{30}=10$.
Answer:
$x = 10$