Let's analyze the problem.

The diagram depicts a quadrilateral $PQRS$, and we need to determine the measure of angle $\angle Q$.

Steps:

1. Sum of interior angles in a quadrilateral: The sum of all angles in a quadrilateral is always $360^\circ$.

   $\angle P + \angle Q + \angle R + \angle S = 360^\circ$

2. Known angles:

   • $\angle P = 90^\circ$
   • $\angle S = 100^\circ$
   • $\angle R = 50^\circ$

3. Substitute known values: $90^\circ + \angle Q + 50^\circ + 100^\circ = 360^\circ$

4. Simplify: $\angle Q + 240^\circ = 360^\circ$

5. Solve for $\angle Q$: $\angle Q = 360^\circ - 240^\circ = 120^\circ$

Final Answer:

The measure of $\angle Q$ is $120^\circ$, so the correct choice is G.

Would you like further clarification or details about this solution?

Related Questions:

1. What is the general formula for the sum of interior angles in polygons with more sides?
2. How would this problem change if one angle in the quadrilateral was unknown, but the sum was not explicitly given?
3. Could the quadrilateral be classified into a specific type based on the angles provided?
4. How can you verify the solution geometrically without computation?
5. What are some real-world applications of knowing the properties of quadrilaterals?

Tip:

Always check that the sum of your calculated angles matches the total interior angle sum for the shape you’re working with. This step ensures accuracy!