Question

In each of the following figures AB is parallel to CD. Find the value of x in each case.

Answer 1

Hey my dear friend.
Here is your answer.

Answer 2

Answer:

In fig 1, x=140°

In fig 2, x=285°

Step-by-step explanation:

Given 2 figures, we have to find out the value of x in each case

In figure 1,

Construct a line OE parallel to AB and CD,then

104°+∠1 = 180°    (∵angle on the same side of transversal)

⇒ ∠1 = 180°-104°=76°

116°+∠2=180°       (∵angle on the same side of transversal)

⇒ ∠2=180°-116°=64°

∠x=∠1+∠2=76°+64°=140°

In figure 2,

∠ABO=∠3=40°    (∵Alternate angles)

∠CDO=∠4=35°    (∵Alternate angles)

Total angle at center O is 360°

⇒ ∠O=∠3+∠4+x

⇒ 360°=40°+35°+x

⇒x=360°-40°-35°=285°