Question

the measures of the exterior angles of an octagon are ( x^{circ}, 3x^{circ}, 4x^{circ}, 5x^{circ}, 6x^{circ}, 7x^{circ}, 9x^{circ} ), and ( 10x^{circ} ). find the measure of the largest exterior angle.

Explanation:

Step1: Use the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\).
So, \(x + 3x+4x + 5x+6x+7x+9x + 10x=360\).

Step2: Combine like terms

\((1 + 3+4 + 5+6+7+9 + 10)x=360\).
\(45x = 360\).

Step3: Solve for \(x\)

\(x=\frac{360}{45}=8\).

Step4: Find the largest exterior angle

The largest exterior angle is \(10x\). Substitute \(x = 8\) into \(10x\).
\(10\times8=80\).

Answer:

\(80^{\circ}\)