In a trapezium ABCD- side AB is parallel to side DC- If - A - x - and - D -3 x -20- value of x - -A- x-20-B- x -60-C- x -80-D- x -50-

The correct option is D x = 50^∘ ∠ A = x^∘ and ∠ D = (3x 20)^∘ ∠ A + ∠ D = 180^∘ (Co interior angles) ⇒ x^∘ + (3x 20)^∘ = 180^∘ ⇒ 4x 20^∘ = 180^∘ ⇒ 4x ...

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Standard VI

Mathematics

Trapezium

In a trapeziu...

Question

In a trapezium ABCD, side AB is parallel to side DC. If $∠ A = x^{\circ}$ and $∠ D = (3 x - 20)^{\circ}$ , value of $x = ?$

$x = 50^{\circ}$

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$x = 60^{\circ}$

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$x = 80^{\circ}$

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$x = 20^{\circ}$

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Solution

The correct option is A
$x = 50^{\circ}$

$∠ A = x^{\circ}$ and $∠ D = (3 x - 20)^{\circ}$

$∠ A + ∠ D = 180^{\circ}$ (Co-interior angles)

$\Rightarrow x^{\circ} + (3 x - 20)^{\circ} = 180^{\circ}$

$\Rightarrow 4 x - 20^{\circ} = 180^{\circ}$

$\Rightarrow 4 x = 180^{\circ} + 20^{\circ}$

$\Rightarrow 4 x = 200^{\circ}$

$\Rightarrow x = 50^{\circ}$

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In a trapezium ABCD, side AB is parallel to side DC. If $∠ A = x^{\circ}$ and $∠ D = (3 x - 20)^{\circ}$ , value of $x = ?$