Question

where PQRS is a rhombus​

Answer 1

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

$angle OSR =\frac{anglePSR}{2}$(Diagonals bisect the angle)

$angle OSR =\frac{100}{2}$

angle OSR = 50 degrees

answers:-

angle OPQ= 40 degrees

angle OSR = 50 degrees

#hope it helps u

#follow me

Answer 2

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.

.

.

.

.

hope this helps you

please mark as brainliest

follow me