Question

in a quadrilateral PQRS, if angle P=60° and angle Q:R:S = 2:3:7 .then find angle S​

Answer 1

Answer:

Answer is attached here

Answer 2

The ∠Q is 50°, ∠R is 75°, ∠S is 175°

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❖ Step-by-step explanation :

❒ Given :-

➠ In a quadrilateral PQRS, if angle P=60° and angle Q:R:S = 2:3:7

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❒ To Find :-

➠ QRS angles in a quadrilateral

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❒ Used Formula :-

$\bf \purple⟼\red{ \: Sum \: of \: all \: angles \: _{(Quadrilateral)}= 360°}$

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❒ Solution :-

In Quadrilateral PQRS,

∠P = 60°

The angles are in ratio Q:R:S = 2:3:7

Let,

Q = 2x

R = 3x

S = 7x

We know that,

Sum of all angles in a Quadrilateral = 360°

So,

$\bf ⟹ \: ∠P + ∠Q + ∠R + ∠S = 360°$

$\bf ⟹ \:60° + 2x + 3x + 7x = 360°$

$\bf ⟹ \: 2x + 3x + 7x = 360° - 60°$

$\bf ⟹ \: 2x + 3x + 7x = 300°$

$\bf ⟹ \: 12x = 300°$

$\displaystyle\bf ⟹ \: x= \cancel\frac{300}{12}$

$\red{⟹ \: \underline{ \boxed{ \bf x = 25}}}$

Now,

➠ ∠P = 60°

➠ ∠Q = 2x = 2×25 = 50°

➠ ∠R = 3x = 3×25 = 75°

➠ ∠S = 7x = 7×25 = 175°

Hence,

The ∠Q is 50°, ∠R is 75°, ∠S is 175°

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❒ Verification :-

$\bf ⟹ \: Sum \: of \: all \: angles \: _{(Quadrilateral)}= 360°$

$\bf ⟹ \: ∠P + ∠Q + ∠R + ∠S = 360°$

$\bf ⟹ \:60° + 50° + 75° + 175° = 360°$

$⟹ \: \boxed{ \bf360°= 360° }$

Hence, verified !

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