Question

1. find the value of x.

Explanation:

Step1: Recall polygon - angle sum formula

The sum of interior angles of an \(n\) - sided polygon is given by \((n - 2)\times180^{\circ}\). For a pentagon (\(n = 5\)), the sum of interior angles is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up an equation

The interior angles of the pentagon are \(x^{\circ},x^{\circ},2x^{\circ},120^{\circ},120^{\circ}\). So, \(x + x+2x + 120+120=540\).

Step3: Combine like - terms

Combining the \(x\) terms and the constant terms, we get \(4x+240 = 540\).

Step4: Solve for \(x\)

Subtract 240 from both sides: \(4x=540 - 240\), so \(4x = 300\). Then divide both sides by 4: \(x=\frac{300}{4}=75\).

Answer:

\(x = 75\)