PQRS is a parallelogram whose diagonals intersect at M- if- PMS-54- QSR-25-and- SQR-30- find-i- RPS-ii- PRS-iii- PSR-

Give : || gm PQRS in which diagonals PR QS intersect at M. ∴ ∠ PMS=54^∘ ; ∠ QSR=25^∘ and ∠ SQR=30^∘ To find : (i) ∠ RPS (ii) ∠ PRS (iii) ∠ PSR Proof : ∵ QR || ...

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Standard VIII

Mathematics

Diagonals of a Parallelogram

PQRS is a par...

Question

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

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Solution

$Give : | | gm PQRS in which diagonals PR & QS intersect at M. ∴ ∠ P M S = 54^{\circ}; ∠ Q S R = 25^{\circ} a n d ∠ S Q R = 30^{\circ}$

$To find : (i) ∠ R P S (i i) ∠ P R S (i i i) ∠ P S R Proof : ∵ Q R | | P S \Rightarrow ∠ P S Q = ∠ S Q R (Alternate ∠ s) B u t ∠ S Q R = 30^{\circ} (Given) ∴ ∠ P S Q = 30^{\circ} I n Δ S M P, ∠ P M S + ∠ P S M + ∠ M P S = 180^{\circ} o r 54^{\circ} + 34^{\circ} + ∠ R P S = 180^{\circ} ∠ R P S = 180^{\circ} - 84^{\circ} = 96^{\circ} N o w ∠ P R S + ∠ R S Q = ∠ P M S ∴ ∠ P R S + 25^{\circ} = 54^{\circ} ∠ P R S = 54^{\circ} - 25^{\circ} = 29^{\circ} ∠ P S R = ∠ P S Q + ∠ R S Q = 30^{\circ} + 25^{\circ} = 55^{\circ} H e n c e (i) ∠ R P S = 96^{\circ} (i i) ∠ P R S = 29^{\circ} (i i i) ∠ P S R = 55^{\circ}$

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Similar questions

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

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

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 .

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 .

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 :

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PQRS is a parallelogram whose diagonals intersect at M.if ∠PMS=54∘, ∠QSR=25∘ and ∠SQR=30∘ ;find : (i) ∠RPS (ii) ∠PRS (iii) ∠PSR.

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