To solve for $x$ in the given diagrams, let's analyze the angles step by step.

Diagram Details:

• In both diagrams, RSU and STV are straight lines.
• The angles given are:
  • $\angle VSP = 70^\circ$
  • $\angle USP = 60^\circ$
  • $\angle QRP = 80^\circ$
  • $\angle PQS = 90^\circ$

Steps to Solve:

1. Angle $\angle SQR$: Since $RSU$ is a straight line, the angles along this line sum up to $180^\circ$.

   $\angle SQR + \angle QRP = 180^\circ$

   Substituting the values:

   $\angle SQR + 80^\circ = 180^\circ$

   $\angle SQR = 180^\circ - 80^\circ = 100^\circ$

2. Angle $\angle PQR$: Since $PQRS$ forms a quadrilateral and the sum of angles in a quadrilateral is $360^\circ$:

   $\angle PQS + \angle SQR + \angle QRP + x = 360^\circ$

   Substituting the known values:

   $90^\circ + 100^\circ + 80^\circ + x = 360^\circ$

   Simplifying:

   $270^\circ + x = 360^\circ$

   $x = 360^\circ - 270^\circ = 90^\circ$

So, the value of $x$ is $\boxed{90^\circ}$.

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Would you like a detailed explanation of any step, or do you have any further questions?

Related Questions:

1. What is the sum of the interior angles of a quadrilateral?
2. How can you verify if a given angle is correct using complementary or supplementary angles?
3. What are the properties of angles formed by a transversal cutting parallel lines?
4. How do you find missing angles in a triangle?
5. What is the relationship between exterior and interior angles in polygons?

Tip: When dealing with straight lines and angles, always remember that the sum of angles around a point is $360^\circ$, and on a straight line, it's $180^\circ$.