In the adjoining figure AB || CD, ∠1 : ∠2 = 3 : 2. Then ∠6 is _____

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In the adjoining figure AB || CD, ∠1 : ∠2 = 3 : 2. Then ∠6 is _____

Options:

A . 72

^{\circ}

B . 36

^{\circ}

C . 100

^{\circ}

D . 144

^{\circ}

Answer: Option A
:
A

Let $∠$ 1 = 3x and $∠$ 2 = 2x

Sum of angles on a straight line is 180 $^{\circ}$ .

So, 3x + 2x = 180 $^{\circ}$

⇒ 5x = 180 $^{\circ}$

⇒ x = 36 $^{\circ}$

⇒ $∠$ 6 = $∠$ 2 [ $∵$ ∠6 and ∠2 are corresponding angles]
⇒ $∠$ 6 = 2x = 2 × 36 = 72 $^{\circ}$

Hence, $∠$ 6 = 72 $^{\circ}$

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