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Standard XII

Mathematics

Condition for Two Lines to Be Parallel

PQRS is a par...

Question

$P Q R S$ is a parallelogram whose diagonals intersect at $M$ .
If $∠ P M S = 54^{o}, ∠ Q S R = 25^{o}$ and $∠ S Q R = 30^{o}$ ; find:
i) $∠ R P S$
ii) $∠ P R S$
iii) $∠ P S R$ .

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Solution

we know that for this parallelogram;
$∠ P M S = ∠ Q S R + ∠ P R S; ∠ S Q R = ∠ P S Q; ∠ R P S + ∠ P M S + ∠ P S M = 180^{\circ} ⟹ ∠ R P S = 96^{\circ}; ∠ P R S = 29^{\circ} ∠ P S R = 55^{\circ}$

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Similar questions

$PQRS is a parallelogram whose diagonals intersect at M. i f ∠ P M S = 54^{\circ}, ∠ Q S R = 25^{\circ} a n d ∠ S Q R = 30^{\circ}; f i n d : (i) ∠ R P S (i i) ∠ P R S (i i i) ∠ P S R .$

Q. PQRS is a parallelogram whose diagonals intersect at M.

∠ P M S = 54^{\circ}, ∠ Q S R = 25^{\circ} and ∠ S Q R = 30^{\circ};

(i) ∠ R P S

(ii) ∠ P R S

(iii) ∠ P S R

Q. The diagonals of a parallelogram PQRS intersect at O. If

∠ Q O R = 90^{\circ} a n d ∠ Q S R = 50^{\circ}, t h e n ∠ O R S

is :

Q. In the given figure,

P Q R S

is a cyclic quadrilateral. Its diagonals

P R

and

Q S

intersect each other at

T

. If

∠ P R S = 80^{\circ} a n d ∠ R Q S = 50^{\circ}

, calculate

∠ P S R

Q. PQRS is a cyclic quadrilateral whose diagonals intersect at A. If

∠ S Q R = 80^{\circ}

and

∠ Q P R = 30^{\circ},

then find

∠ S R Q .

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PQRS is a parallelogram whose diagonals intersect at M.If ∠PMS=54o,∠QSR=25o and ∠SQR=30o; find:i) ∠RPSii) ∠PRSiii) ∠PSR.

we know that for this parallelogram;∠PMS=∠QSR+∠PRS;∠SQR=∠PSQ;∠RPS+∠PMS+∠PSM=180∘⟹∠RPS=96∘;∠PRS=29∘∠PSR=55∘

$P Q R S$ is a parallelogram whose diagonals intersect at $M$ .
If $∠ P M S = 54^{o}, ∠ Q S R = 25^{o}$ and $∠ S Q R = 30^{o}$ ; find:
i) $∠ R P S$
ii) $∠ P R S$
iii) $∠ P S R$ .

we know that for this parallelogram;
$∠ P M S = ∠ Q S R + ∠ P R S; ∠ S Q R = ∠ P S Q; ∠ R P S + ∠ P M S + ∠ P S M = 180^{\circ} ⟹ ∠ R P S = 96^{\circ}; ∠ P R S = 29^{\circ} ∠ P S R = 55^{\circ}$