Question

1. a pentagon has exterior angle measures of 5x°, 10x°, 4x°, 8x° and 3x°. find x.

Explanation:

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^\circ\). For a pentagon, we sum up all the given exterior angles and set it equal to \(360^\circ\).
The exterior angles are \(5x^\circ\), \(10x^\circ\), \(4x^\circ\), \(8x^\circ\) and \(3x^\circ\). So, the equation is \(5x + 10x+4x + 8x+3x=360\).

Step2: Combine like terms

Combine the terms on the left - hand side:
\((5 + 10+4 + 8+3)x=360\)
\(30x = 360\)

Step3: Solve for \(x\)

Divide both sides of the equation \(30x = 360\) by 30:
\(x=\frac{360}{30}\)
\(x = 12\)

Answer:

\(x = 12\)