Question

In the given figure, AB CD and ∠1 and ∠2 are in the ratio 3:2 Determine all angles form 1 to 8.

Answer 1

The given figure is as follows:

It is give that the lines AB and CD are parallel and angles 1 and 2 are in the ratio 3: 2.

Let

In the figure angle 1 and 2 are supplementary. So,

3x + 2x = 180

⇒ 5x = 180

⇒ x = 36
$\angle 1=36\times 3=108°\mathrm{and}\angle 2=36\times 2=72°$

Since, angle 1 and 5 and angle 2 and 6 are corresponding angles, so

Since, angles 1 and 3 and 2 and 4 are vertically opposite angles, so

Now,

Angle 5 and 6 and angle 6 and 8 are vertically opposite angles, so

Hence,and.