Question

q1: mathspace assignment #4: q... 3. solve for the value of x in the diagram below. enter each line of work as an equation.

Explanation:

Step1: Recall sum of angles in quadrilateral

The sum of interior angles of a quadrilateral is $360^{\circ}$.

Step2: Set up equation

We have the equation $99 + 55+x + y=360$, where $y$ is the fourth - angle. Since we assume the two non - given angles are equal (as no other information is provided about the shape being non - symmetric), we can rewrite it as $99+55 + 2x=360$.

Step3: Simplify left - hand side

$154 + 2x=360$.

Step4: Isolate the term with $x$

Subtract 154 from both sides: $2x=360 - 154$. So, $2x = 206$.

Step5: Solve for $x$

Divide both sides by 2: $x=\frac{206}{2}=103$.

Answer:

$x = 103$