Question

the measures of the exterior angles of a triangle are (5x^{circ}), (9x^{circ}), and (10x^{circ}). find the measure of the smallest exterior angle.

Explanation:

Step1: Use the exterior angle sum property

The sum of exterior angles of any polygon is \(360^{\circ}\). For a triangle, \(5x + 9x+10x=360\).

Step2: Solve for \(x\)

Combine like - terms: \(24x = 360\). Then \(x=\frac{360}{24}=15\).

Step3: Find the measure of each exterior angle

The exterior angles are \(5x = 5\times15 = 75^{\circ}\), \(9x=9\times15 = 135^{\circ}\), \(10x = 10\times15=150^{\circ}\).

Answer:

\(75\)