Question

question 9 of 12
the convex polygon below has 5 sides. find the value of x.
(5 - 2) 3.180 \frac{540}{5}=180
135° 106°
81°
110°
x°

Explanation:

Step1: Calculate the sum of interior angles

The formula for the sum of interior angles of an \(n\) - sided polygon is \((n - 2)\times180^{\circ}\). For \(n = 5\), the sum \(S=(5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

We know that \(81^{\circ}+135^{\circ}+106^{\circ}+110^{\circ}+x^{\circ}=540^{\circ}\).

Step3: Solve for \(x\)

First, add the known angles: \(81 + 135+106 + 110=432\). Then, \(x=540 - 432\).

Answer:

\(x = 108\)