Question

find the value of x.

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is \(360^\circ\).

Step2: Set up the equation

Let the four angles be \(52^\circ\), \(130^\circ\), \(91^\circ\), and \(x^\circ\). Then we have the equation:
\(52 + 130 + 91 + x = 360\)

Step3: Simplify the left - hand side

First, calculate the sum of the known angles: \(52+130 + 91=273\). So the equation becomes \(273+x = 360\).

Step4: Solve for x

Subtract 273 from both sides of the equation: \(x=360 - 273\).
\(x = 87\)

Answer:

\(x = 87\)