Question

the measures of the exterior angles of a quadrilateral are ( x^{circ}, 2x^{circ}, 4x^{circ} ), and ( 5x^{circ} ). find the measure of the smallest exterior angle.

Explanation:

Step1: Use the formula for the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\). So, \(x + 2x+4x + 5x=360\).

Step2: Combine like - terms

Combining the left - hand side terms: \((1 + 2+4 + 5)x=360\), which simplifies to \(12x = 360\).

Step3: Solve for \(x\)

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

Answer:

The measure of the smallest exterior angle is \(30^{\circ}\).