Question

the measures of the exterior angles of a quadrilateral are ( 3x^{circ},4x^{circ},8x^{circ} ), and ( 9x^{circ} ). solve for ( x ).

Explanation:

Step1: Use the exterior angle sum property

The sum of the exterior angles of any polygon is \(360^{\circ}\). For a quadrilateral, we have \(3x + 4x+8x + 9x=360\).

Step2: Combine like terms

Combining the \(x\) - terms: \((3 + 4+8 + 9)x=360\). Since \(3+4 + 8+9=24\), the equation becomes \(24x = 360\).

Step3: Solve for \(x\)

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

Answer:

\(x = 15\)