In the figure ABCD is a trapezium. Find the values of $x$ and $y$ .

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Solution

In trapezium ABCD, $A B | | C D$

$∴ ∠ A + ∠ D = 180^{\circ}$ (Sum of cointerior angles)

$x + 20^{\circ} + 2 x + 10^{\circ} = 180^{\circ}$
$3 x + 30 x^{\circ} = 180^{\circ} \Rightarrow 3 x = 180^{\circ} - 30^{\circ}$
$\Rightarrow 3 x = 150^{\circ}$
$∴ x = \frac{150^{\circ}}{3} = 50^{\circ}$

Similarly, $∠ B + ∠ C = 180^{\circ}$

$\Rightarrow y + 92^{\circ} = 180^{\circ} \Rightarrow y = 180^{\circ} - 92^{\circ} ∴ y = 88^{\circ}$

Hence, $x = 50^{\circ}, y = 88^{\circ}$

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In the figure ABCD is a trapezium. Find the values of x and y.

In trapezium ABCD, AB||CD ∴∠A+∠D=180∘ (Sum of cointerior angles) x+20∘+2x+10∘=180∘3x+30x∘=180∘⇒3x=180∘−30∘⇒3x=150∘∴x=150∘3=50∘ Similarly, ∠B+∠C=180∘ ⇒y+92∘=180∘⇒y=180∘−92∘∴y=88∘ Hence, x=50∘,y=88∘

In the figure ABCD is a trapezium. Find the values of $x$ and $y$ .