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 \((n - 2)\times180^{\circ}\). Here \(n = 5\), so the sum of interior angles is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up an equation

We know that \(87^{\circ}+105^{\circ}+135^{\circ}+92^{\circ}+x^{\circ}=540^{\circ}\).

Step3: Simplify the left - hand side

\((87 + 105+135 + 92)+x=540\), \(419+x = 540\).

Step4: Solve for \(x\)

Subtract 419 from both sides: \(x=540 - 419\), \(x = 121\).

Answer:

\(121\)