In parallelogram PQRS- Q-4x-5-and- S-3x-10-Calculate - Q-and- R-

In parallelogram PQRS, ∠ Q=(4x 5)^∘ and ∠ S=(3x+10)^∘ ∵ opposite ∠ s of || gm are equal. ∴ ∠ Q = ∠ S 4x 5=3x+10 4x 3x=10+5 x=15 ∴ ∠ Q=4x 5=4× 15 5=55^∘ ...

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Standard VIII

Mathematics

Angles of a Parallelogram

In parallelog...

Question

$In parallelogram PQRS, ∠ Q = (4 x - 5)^{\circ} a n d ∠ S = (3 x + 10)^{\circ} . Calculate : ∠ Q a n d ∠ R .$

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Solution

$In parallelogram PQRS,$

$∠ Q = (4 x - 5)^{\circ} a n d ∠ S = (3 x + 10)^{\circ}$

$∵ o p p o s i t e ∠ s o f | | gm are equal. ∴ ∠ Q = ∠ S 4 x - 5 = 3 x + 10 4 x - 3 x = 10 + 5 x = 15 ∴ ∠ Q = 4 x - 5 = 4 \times 15 - 5 = 55^{\circ} A l s o ∠ Q + ∠ R = 180^{\circ} 55^{\circ} + ∠ R = 180^{\circ} ∠ R = 180^{\circ} - 55^{\circ} = 125^{\circ} ∴ ∠ Q = 55^{\circ}; ∠ R = 125^{\circ}$

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In parallelogram PQRS, ∠Q=(4x−5)∘ and∠S=(3x+10)∘.Calculate : ∠Q and ∠R.

In parallelogram PQRS, ∠Q=(4x−5)∘ and ∠S=(3x+10)∘ ∵ opposite ∠s of || gm are equal.∴ ∠Q = ∠S 4x−5=3x+104x−3x=10+5x=15∴ ∠Q=4x−5=4×15−5=55∘Also ∠Q+∠R=180∘ 55∘+∠R=180∘ ∠R=180∘−55∘=125∘∴ ∠Q=55∘ ; ∠R=125∘

$In parallelogram PQRS, ∠ Q = (4 x - 5)^{\circ} a n d ∠ S = (3 x + 10)^{\circ} . Calculate : ∠ Q a n d ∠ R .$