Question

XERCESE 6.2 1. In Fig. 6.28, find the values of x and y and then show that AB | CD.​

Answer 1

Answer:

Here, ∠x+50

Here, ∠x+50 0

Here, ∠x+50 0 =180

Here, ∠x+50 0 =180 0

Here, ∠x+50 0 =180 0 --- straight line

Here, ∠x+50 0 =180 0 --- straight line∠x=180

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite angles

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite anglesThus, ∠x=∠y=130

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite anglesThus, ∠x=∠y=130 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite anglesThus, ∠x=∠y=130 0

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite anglesThus, ∠x=∠y=130 0 Using Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.

Here, ∠x+50 0 =180 0 --- straight line∠x=180 0 −50 0 ∠x=130 0 And ∠y=130 0 --- vertically opposite anglesThus, ∠x=∠y=130 0 Using Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.Thus, AB∥CD

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