Question

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Explanation:

Step1: Recall the formula for the sum of interior angles of a hexagon

The sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For \(n = 6\), the sum \(S=(6 - 2)\times180^{\circ}=720^{\circ}\).

Step2: Set up an equation based on the given angles

We have the equation \(120^{\circ}+150^{\circ}+x + 135^{\circ}+105^{\circ}+125^{\circ}=720^{\circ}\).

Step3: Simplify the left - hand side of the equation

Combine the known angles: \(120 + 150+135 + 105+125=635\). So the equation becomes \(635^{\circ}+x=720^{\circ}\).

Step4: Solve for \(x\)

Subtract \(635^{\circ}\) from both sides: \(x=720^{\circ}-635^{\circ}\).

Answer:

\(x = 85^{\circ}\)