Question

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

• A. 72${}^{\circ }$
• B. 36${}^{\circ }$
• C. 100${}^{\circ }$
• D. 144${}^{\circ }$

Answer 1

The correct option is A

72${}^{\circ }$

Let $\angle$1 = 3x and $\angle$2 = 2x

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

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

⇒ 5x = 180${}^{\circ }$

⇒ x = 36${}^{\circ }$

⇒$\angle$6 = $\angle$2 [$\because$∠6 and ∠2 are corresponding angles]

⇒ $\angle$6 = 2x = 2 × 36 = 72${}^{\circ }$

Hence, $\angle$6 = 72${}^{\circ }$