Question

using the polygon sum and linear pairs, solve for x.

Explanation:

Step1: Calculate the sum of interior angles of a pentagon

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

Step2: Set up an equation

Let the unknown interior angle adjacent to \(x\) be \(y\). We know that \(125 + 95+105 + 95+y=540\).
Simplify the left - hand side: \(125+95 + 105+95+y=(125 + 105)+(95\times2)+y=230 + 190+y=420 + y\).
Then \(420 + y=540\), so \(y = 540-420=120^{\circ}\).

Step3: Use the linear - pair relationship

Since \(x\) and \(y\) form a linear pair (\(x + y=180^{\circ}\)), and \(y = 120^{\circ}\), then \(x=180 - 120\).

Answer:

\(60\)