Question

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

Answer 1

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

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

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

⇒ 5x = 180${}^{\circ }$

⇒ x = 36${}^{\circ }$ [1 Mark]

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

⇒ $\angle 6=2x=2\times {36}^{\circ }={72}^{\circ }$
Hence, $\angle 6={72}^{\circ }$. [1 Mark]