Q. 45.0( 6 Votes )

By calculating, I write the values of X and Y in the following rectangle PQRS:


Answer :

Given PQRS is a rectangle


Each angle of a rectangle is 90°


Let O be the intersecting point of PR and QS


(i) SQR = 25°(given)


⇒∠PQS = 90° - 25° = 65°


And PSQ = 25° = SQR and QSR = PQS = 65°(PS QR and QS is transversal) and


Since the diagonals of rectangle are equal and bisects each other


In ΔQOR


OQ = OR


OQR = QRO = 25° (angles opposite to equal sides are equal)


QOR = 40° (angle sum property of a triangle)


SRQ = 90° (Each angle of a rectangle is 90°)


And QRP = 25° so PRS = x = 90° - 25° = 65°


In Δ PSO


PSQ = 25° and SPR = 25°


⇒∠POS = y = 90° - 50° = 40° (angle sum property of a triangle)


(ii) In rectangle PQRS


QOR = POS = 100° (vertically opposite angles)


In ΔPOS


PO = OS (diagonals of a rectangle are equal and bisects each other)


OPS = OSP = y


y = 180° - 100° =


x = 50°( each angle of rectangle is 90°)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Properties of ParallelogramQuiz | Properties of ParallelogramQuiz | Properties of Parallelogram31 mins
Champ Quiz | Area of ParallelogramChamp Quiz | Area of ParallelogramChamp Quiz | Area of Parallelogram55 mins
Quiz | Area and ParallelogramQuiz | Area and ParallelogramQuiz | Area and Parallelogram46 mins
NCERT |  Imp. Qs. on Area of Parallelogram and TrianglesNCERT |  Imp. Qs. on Area of Parallelogram and TrianglesNCERT | Imp. Qs. on Area of Parallelogram and Triangles43 mins
Quiz | Area of Parallelogram and TrianglesQuiz | Area of Parallelogram and TrianglesQuiz | Area of Parallelogram and Triangles43 mins
NCERT |  Imp Qs on Area of Parallelogram And TrianglesNCERT |  Imp Qs on Area of Parallelogram And TrianglesNCERT | Imp Qs on Area of Parallelogram And Triangles44 mins
Champ Quiz | Solution - Types & PropertiesChamp Quiz | Solution - Types & PropertiesChamp Quiz | Solution - Types & Properties46 mins
Quiz | Master The Interconversion of States of MatterQuiz | Master The Interconversion of States of MatterQuiz | Master The Interconversion of States of Matter53 mins
Proof of Important Theorems of CirclesProof of Important Theorems of CirclesProof of Important Theorems of Circles46 mins
Applications of Newton's First Law of MotionApplications of Newton's First Law of MotionApplications of Newton's First Law of Motion53 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses