Question

the measures of the exterior angles of an octagon are (2x^{circ}), (3x^{circ}), (4x^{circ}), (5x^{circ}), (6x^{circ}), (7x^{circ}), (8x^{circ}), and (10x^{circ}). find the measure of the largest exterior angle.

Explanation:

Step1: Recall the sum of exterior angles of a polygon

The sum of the exterior angles of any polygon is \(360^{\circ}\).

Step2: Set up an equation

We have the exterior angles \(2x^{\circ},3x^{\circ},4x^{\circ},5x^{\circ},6x^{\circ},7x^{\circ},8x^{\circ},10x^{\circ}\).
So, \(2x + 3x+4x + 5x+6x+7x+8x + 10x=360\).
Combine like terms: \((2 + 3+4 + 5+6+7+8 + 10)x=360\).
\(45x = 360\).

Step3: Solve for \(x\)

Divide both sides by \(45\): \(x=\frac{360}{45}=8\).

Step4: Find the largest exterior angle

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

Answer:

\(80^{\circ}\)