In the figure given below, AB is parallel to CD. Find the measures of x and y.

30^{\circ}, 20^{\circ}

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20^{\circ}, 30^{\circ}

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20^{\circ}, 20^{\circ}

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30^{\circ}, 30^{\circ}

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Solution

The correct option is C $20^{\circ}, 20^{\circ}$

It is given that lines AB and CD are parallel to each other.
We know that when two parallel lines are cut by a transversal, the pairs of alternate interior angles are equal.

So, ∠AEC = ∠DCE = 40° [Alternate interior angles]
$2 x = 40 °$
$x = \frac{40 °}{2} = 20 °$

Also, ∠BED = ∠CDE =60° [Alternate interior angles]
$3 y = 60 °$
$y = \frac{60 °}{3} = 20 °$
Hence, the respective values of x and y are 20° and 20°.

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If $x = 20^{\circ}$ and $y = 30^{\circ}$ in the given figure, find the value of z.

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C.I.	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
f	$5$	$x$	$20$	$14$	$y$	$8$	$68$

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Class-interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	Total
Frequency	$5$	$x$	$20$	$15$	$y$	$5$	$60$

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