Question

if a transversal intersects two parallel lines and the difference of two interior angles on the same side of a transversal is 20 degree find the angles

Answer 1

$\textbf{ \underline{ Hello Mate! }}$

Please see once attatchement.

Here, /_ 1 + /_2 = 180° [ Sum of consecutive interior angle ] ----(i)

As mentioned in question, their difference is 20°

/_1 - /_2 = 20° ------(ii)

On adding equation (i) and (ii) we get,

2/_1 = 200° or /_1 = 200° / 2

/_1 = 100°

So, /_2 = 180° - /_1
/_2 = 180° - 100° or 80°

So, /_BOE = /_1 = 100° [ Vertically Opposite Angle ]
/_EDG = /_2 = 80° [ Vertically Opposite Angle ]

/_AOE = /_2 = 80° [Corresponding angle]
/_AOD = /_1 = 100° [Corresponding angle]

/_BOD = /_2 = 80° [ Alternate Angles ]
/_ODC = /_1 = 100° [ Alternate Angles ]

Hence, all angles are been taken out.

Have great future ahead!