In figure, which of the lines are parallel to each other and why? Give

1.	In figure, which of the lines are parallel to each other and why? Give reasons?
Answer» As we know that if a number of lines meet at a point then the sum of all the angles so formed = 360° Here ∠PAQ + ∠QAB + reflex ∠PAB = 360° ⇒ 55° + ∠QAB + 255° = 360° ⇒ ∠QAB = 360° – 310° ⇒ ∠QAB = 50° ⇒ ∠QAB = ∠ABR = 50° (alt. angle) QA \|\| BR Also ∠PAB = ∠ABS = 105° (alt. angles) PA \|\| BS Hence QA \|\| BR and PA \|\| BS.

In figure, which of the lines are parallel to each other and why? Give reasons?

Answer»

As we know that if a number of lines meet at a point then the sum of all the angles so formed = 360°

Here

∠PAQ + ∠QAB + reflex ∠PAB = 360°

⇒ 55° + ∠QAB + 255° = 360°

⇒ ∠QAB = 360° – 310°

⇒ ∠QAB = 50°

⇒ ∠QAB = ∠ABR = 50° (alt. angle)

QA || BR

Also ∠PAB = ∠ABS = 105° (alt. angles)

PA || BS

Hence QA || BR and PA || BS.