Question

the measures of the exterior angles of a pentagon are $x^circ$, $3x^circ$, $4x^circ$, $5x^circ$, and $7x^circ$. find the measure of the largest exterior angle.

answer attempt 1 out of 2

Explanation:

Step1: Recall exterior angle sum

The sum of exterior angles of any polygon is \(360^\circ\). For a pentagon, sum of \(x^\circ, 3x^\circ, 4x^\circ, 5x^\circ, 7x^\circ\) is \(360^\circ\).

$$x + 3x + 4x + 5x + 7x = 360$$

Step2: Combine like terms

Combine the \(x\) terms: \( (1 + 3 + 4 + 5 + 7)x = 360 \)

$$20x = 360$$

Step3: Solve for \(x\)

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

Step4: Find largest exterior angle

Largest exterior angle is \(7x^\circ\). Substitute \(x = 18\):

$$7 \times 18 = 126$$

Answer:

\(126^\circ\)