where PQRS is a rhombus

Answers
Given:-
PQRS is a rhombus
to find :-
angle OSR
angle OPQ
value :-
PS // QR (opp. side of rhombus are equal and parallel)
therefore:
PR is a transversal
angle ORS = angle OPQ ( vertically opp. angles)
angle OPQ= 40 degrees
In triangle PRS
PS=SR(all sides of a rhombus are equal)
therefore angle SRP = angle SPR(equal angle have equal sides opp to it)
angle SRP + angle SPR + angle PSR = 180(sum of all angles of triangle is 180)
40+40+PSR = 180
PSR = 180-80
PSR = 100
(Diagonals bisect the angle)
angle OSR = 50 degrees
answers:-
angle OPQ= 40 degrees
angle OSR = 50 degrees
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Step-by-step explanation:
◆Case-I
Given that,
PQRS is a rhombus
angle ORS=40°
we know that in a rhombus the diagonals are equal and parallel.
so,
angle ORS= angle OPQ= y = 40°
and the intersection of diagonal at point O be 90°angle --»SOR=ROQ=QOP=POS=90°
so in ∆ORS,
we have,
angle sum property of a triangle is 180°.
so,
angle ORS
=>180°-angle(OR+SOR)
=>180°-(40°+90°)
=>180°-130°
=>50°
so, angle ORS=x=50°
Hence,x=50°,y=40°.
case-II
we can also find the values of x and y by proving the rhombus equal to the parallelogram , and then by using the properties of parallelogram we can obtain the value of of x and y.
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