Q Find value of x and y in the following figure (ii) where PQRS is a rhombus - Maths - Understanding Quadrilaterals

Question

Q Find value of x and y in the following figure (ii) where PQRS is
a rhombus

Shruti Tyagi · Accepted Answer

Dear student,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5abc67e27b822%20jpg"
style="width: 206px; height: 172px;">
We know that in rhombus, diagonal bisect each other aSt 90°∴∠SOR=∠POS=90°In ∆SOR∠RSO+∠SOR+∠SRO=180°⇒x+90°+40°=180°⇒x=180°-130°⇒x=50°Also, in rhombus opposite sides of rhombus are parallel
∴SR∥PQ and PS∥QRwhen SR∥PQ⇒∠RPQ =∠SRP    --(alternate interior angle)⇒y=40°
Thus the value of x and y are 50° and 40°
respectively

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Q. Find value of x and y in the following figure (ii) where PQRS is a rhombus.