Question

the measures of the exterior angles of a quadrilateral are $2x^{circ}$, $3x^{circ}$, $9x^{circ}$, and $10x^{circ}$. find the measure of the largest exterior angle.

Explanation:

Step1: Recall the sum of exterior angles of a quadrilateral

The sum of the exterior angles of any polygon is \(360^\circ\). For a quadrilateral, the sum of its exterior angles is also \(360^\circ\). So we can set up the equation: \(2x + 3x+9x + 10x=360\).

Step2: Combine like terms

Combine the \(x\) terms on the left side: \((2 + 3+9 + 10)x=360\), which simplifies to \(24x = 360\).

Step3: Solve for \(x\)

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

Step4: Find the largest exterior angle

The largest exterior angle is \(10x^\circ\). Substitute \(x = 15\) into \(10x\): \(10\times15 = 150\).

Answer:

The measure of the largest exterior angle is \(150^\circ\)