Question

the measures of the exterior angles of a quadrilateral are ( 2x^{circ},4x^{circ},5x^{circ} ), and ( 7x^{circ} ). find the measure of the largest exterior angle.
answer
attempt 1 out of 2

Explanation:

Step1: Use the exterior angle sum property

The sum of exterior angles of any polygon is \(360^{\circ}\). For a quadrilateral, we have \(2x + 4x+5x + 7x=360\).

Step2: Simplify the left - hand side

Combining like terms, \((2 + 4+5 + 7)x=18x\). So, \(18x = 360\).

Step3: Solve for \(x\)

Divide both sides by \(18\): \(x=\frac{360}{18}=20\).

Step4: Find the measure of the largest exterior angle

The largest exterior angle is \(7x\). Substitute \(x = 20\) into \(7x\), we get \(7\times20 = 140\).

Answer:

\(140^{\circ}\)