Angles of a quadrilateral are given as 85- 95- x - x -10- Find the value of x-A- 75- 85-C- 65-D- 105-

The correct option is B 85^∘ ∵ Sum of interior angles of a quadrilateral = 360^∘ ⇒ 85^∘ + 95^∘ + x^∘ + (x + 10)^∘ = 360^∘ ⇒ 180^∘ + x^∘ + x^∘ + 10^∘ = 360^∘ ⇒ ...

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Byju's Answer

Standard IX

Mathematics

Angle Sum Property of a Quadrilateral

Angles of a q...

Question

Angles of a quadrilateral are given as $85^{\circ}, 95^{\circ}, x^{\circ}, (x + 10)^{\circ}$ .
Find the value of $x$ .

$75^{\circ}$

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$85^{\circ}$

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$65^{\circ}$

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$105^{\circ}$

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Solution

The correct option is B
$85^{\circ}$

$∵$ Sum of interior angles of a quadrilateral $= 360^{\circ}$

$\Rightarrow 85^{\circ} + 95^{\circ} + x^{\circ} + (x + 10)^{\circ} = 360^{\circ}$

$\Rightarrow 180^{\circ} + x^{\circ} + x^{\circ} + 10^{\circ} = 360^{\circ}$

$\Rightarrow 190^{\circ} + 2 x^{\circ} = 360^{\circ}$

$\Rightarrow 2 x^{\circ} = 360^{\circ} - 190^{\circ} = 170^{\circ}$

$\Rightarrow x^{\circ} = \frac{170^{\circ}}{2}$

$\Rightarrow x^{\circ} = 85^{\circ}$

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Angles of a quadrilateral are given as 85∘, 95∘, x∘, (x+10)∘. Find the value of x.

The correct option is B 85∘ ∵ Sum of interior angles of a quadrilateral =360∘ ⇒85∘+95∘+x∘+(x+10)∘=360∘ ⇒180∘+x∘+x∘+10∘=360∘ ⇒190∘+2x∘=360∘ ⇒2x∘=360∘−190∘=170∘ ⇒x∘=170∘2 ⇒x∘=85∘

Angles of a quadrilateral are given as $85^{\circ}, 95^{\circ}, x^{\circ}, (x + 10)^{\circ}$ .
Find the value of $x$ .