Question

If the given figure AB||CD. Find the value of x.​

Answer 1

Step-by-step explanation:

Given :-

AB || CD

To find :-

Find the value of x ?

Construction:-

Draw a line EF parallel to AB and CD.

Solution :-

EF || AB and BE is a transversal then

<ABE and <FEB are the interior angles on the same side to the transversal which are supplementary.

=> <ABE + <FEB = 180°

=> 120° + <FEB = 180°

=> <FEB = 180°-120°

=> <FEB = 60°

and

EF || CD and DE is a transversal then

< CDE and <DEF are the interior angles on the same side to the transversal which are supplementary.

=> < CDE + <DEF = 180°

=> 140°+ <DEF = 180°

=> <DEF = 180°-140°

=> < DEF = 40°

Now,

<BED = <BEF + <DEF

=> x = 60°+40°

=> x = 100°

Therefore, x = 100°

Answer:-

The value of x for the given problem is 100°

Used formulae:-

If two parallel lines are Intersected by a transversal then

→ The interior angles on the same side to the transversal are supplementary.