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 with several angles provided:
The straight line is also noted, where is adjacent to angle .
To find , we can use the fact that angles on a straight line sum to . Since and are supplementary (they are on the straight line ):
Thus,
Therefore, .
Would you like more details or explanations? Here are five related questions you might consider:
- How do we find the sum of interior angles in a quadrilateral?
- How can you check if a quadrilateral is cyclic, using angles?
- What is the relationship between supplementary and adjacent angles?
- Can we verify the other angles in the quadrilateral using angle sum properties?
- How can we calculate exterior angles of polygons?
Tip: Always remember that adjacent angles on a straight line add up to .
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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