Question 40

In the given figure, PQ ||ST. Then the value of x + y is

(a) $125^{\circ}$
(b) $135^{\circ}$
(c) $145^{\circ}$
(d) $120^{\circ}$

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Solution

Since, PQ || ST, then PO will also parallel to ST.
Now, PO || ST and OS is transversal,
Therefore,
$x = 85^{\circ}$ [alternate interior angles]
Now $y + 130^{\circ} = 180^{\circ} [l i n e a r p a i r] \Rightarrow y = 180^{\circ} - 130^{\circ} \Rightarrow y = 50^{\circ} ∴ x + y = 85^{\circ} + 50^{\circ} = 135^{\circ}$

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P Q | | S T, T V | | R S a n d T U ⊥ S T .

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Question 33

In the given figure, $a = 40^{\circ}$ . The value of b is

(a) $20^{\circ}$
(b) $24^{\circ}$
(c) $36^{\circ}$
(d) $120^{\circ}$

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