Question

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chapter -Parallel line
class8 question

Answer 1

1. Produce A lineAB parallel to line PQ I.e alternative angle

Answer 2

c)
 Given,
        AB ║ PQ 
To find :- Angle y 
                   By transversal method:-
                                                   Extend line segment AR and PR
   Mark the point where it intersects AB as y.
∠AXR = 59°      [∵ ∠AXR and ∠RPQ are vertically opposite angle 
                           ∴ ∠AXR = ∠RPQ ]

In Δ AXR,
       ∠ XAR = 59°     [given]
       ∠ AXR = 59° 
and ∠ ARX = 180 - (59+59) = 62°

∴ ∠ y = 180 - ∠ARX 
         = 180 - 62 
         = 118

∴ ∠ y = 118 ° 

d)
∵ AC ║ DF and DE is a transversal of it,
∠ y = 180 - 60             [ co-interior angles ]
      = 120
∠ ABC  =  180 -110 = 70°   [co-interior angles]
∴  ∠ x = 180 -  70 = 110°  [co-interior angles]

e)
(5x + 35) + 45 =  180       [co-interior angles]

⇒  5x + 35 = 180 – 45

⇒ 5x =  135 – 35

⇒ x = 100/5
∴ x = 20

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I'm also attaching some pics of the solution and the figures.