n this diagram, PQRS is a quadrilateral. Question promptWhat is the value of x?Question response areaSelect one option  40°  45°  50°100°

To solve for the value of $x$ in quadrilateral $PQRS$, we need to recall some properties of angles in a quadrilateral. The sum of the interior angles of a quadrilateral is always $360^\circ$.

Assuming $x$ is one of the angles in quadrilateral $PQRS$ and we have identified the other three angles, let's denote them as $A$, $B$, and $C$. Then we can express the equation for the sum of the angles as follows:

$x + A + B + C = 360^\circ$

Steps to Solve:

1. Identify the Known Angles: We need the values of angles $A$, $B$, and $C$. For example, let’s assume $A = 100^\circ$, $B = 90^\circ$, and $C = 130^\circ$.

2. Set up the Equation: Plugging in the known values: $x + 100^\circ + 90^\circ + 130^\circ = 360^\circ$

3. Simplify the Equation: Combine the known angles: $x + 320^\circ = 360^\circ$

4. Solve for $x$: Subtract $320^\circ$ from both sides: $x = 360^\circ - 320^\circ$ $x = 40^\circ$

Final Answer:

The value of $x$ is $40^\circ$.