In the given figure MN and PQ are parallel, find $X + Y$ .

105

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Solution

The correct option is A 105
Consider parallel lines MN and PQ and PN as transversal.
$∠ Q P N = ∠ M N P$
[Alternate interior angles are equal]
$X = 30^{\circ} ∠ N M Q = ∠ P Q M ∠ N M Q = 45^{\circ} Y = ∠ N M Q + ∠ M N P$ [Exterior angle property]
$Y = 45^{\circ} + 30^{\circ} Y = 75^{\circ}$

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Question 105(i)

In the given figure, PQ, RS and UT are parallel lines.

If $c = 57^{\circ} a n d a = \frac{c}{3}$ , find the value of d.

A B ∥ P Q ∥ C D

A B = x

C D = y

P Q = z

\frac{1}{x} + \frac{1}{y} = \frac{1}{z}

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