Math Problem Statement

In quadrilateral PQRS, angles are given as ∠P = 95°, ∠Q = 130°, ∠R = 65°, and PST is a straight line. Find the value of angle PSR (y°).

Solution

The diagram you uploaded shows a quadrilateral PQRSPQRS with several angles provided:

  • P=95\angle P = 95^\circ
  • Q=130\angle Q = 130^\circ
  • R=65\angle R = 65^\circ

The straight line PSTPST is also noted, where PSR=y\angle PSR = y^\circ is adjacent to angle P\angle P.

To find yy^\circ, we can use the fact that angles on a straight line sum to 180180^\circ. Since P=95\angle P = 95^\circ and PSR\angle PSR are supplementary (they are on the straight line PSTPST):

y+95=180y + 95^\circ = 180^\circ

Thus,

y=18095=85y = 180^\circ - 95^\circ = 85^\circ

Therefore, y=85y = 85^\circ.

Would you like more details or explanations? Here are five related questions you might consider:

  1. How do we find the sum of interior angles in a quadrilateral?
  2. How can you check if a quadrilateral is cyclic, using angles?
  3. What is the relationship between supplementary and adjacent angles?
  4. Can we verify the other angles in the quadrilateral using angle sum properties?
  5. How can we calculate exterior angles of polygons?

Tip: Always remember that adjacent angles on a straight line add up to 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in Quadrilaterals
Supplementary Angles

Formulas

Sum of angles on a straight line: ∠P + ∠PSR = 180°

Theorems

Supplementary angles
Angle sum property of quadrilaterals

Suitable Grade Level

Grades 7-9