Question

question
the measures of the exterior angles of a pentagon are 2x°, 3x°, 4x°, 6x°, and 9x°. solve for x.
answer attempt 1 out of 2
x =
submit answer

Explanation:

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Set up the equation

Given the exterior angles \(2x^{\circ},3x^{\circ},4x^{\circ},6x^{\circ},9x^{\circ}\), we have the equation \(2x + 3x+4x + 6x+9x=360\).

Step3: Combine like - terms

\((2 + 3+4 + 6+9)x=360\), so \(24x = 360\).

Step4: Solve for \(x\)

Divide both sides of the equation by \(24\): \(x=\frac{360}{24}=15\).

Answer:

\(15\)