Find the value of X in the figure below:

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100

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Solution

The correct option is A
80

We know that,

$∠ A B C + ∠ C A B + ∠ A C B = 180^{\circ}$ (angle sum property)

$\Rightarrow 90^{\circ} + 50^{\circ} + ∠ A C B = 180^{\circ}$

$\Rightarrow ∠ A C B = 40^{\circ}$

$\Rightarrow ∠ K C L = ∠ A C B = 40^{\circ}$ (vertically opposite angles)

$\Rightarrow ∠ K C L + ∠ C L K + ∠ X = 180^{\circ}$

$\Rightarrow 40^{\circ} + 60^{\circ} + ∠ X = 180^{\circ}$

$\Rightarrow ∠ X = 80^{\circ}$

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Marks	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
Students	$12$	$10$	$24$	$5$	$9$

∠ A B C = 69^{\circ}

∠ A C B = 31^{\circ} .

∠ B D C .

∠ A C D = 120^{\circ}

∠ B C D

∠ A B C = 60^{\circ}, A C = C D

∠ A D E = 150^{\circ} .

∠ B A C .

x

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