Question

In the given figure, AB || CD || EF intersected by a transversal PQ at X, Y and Z respectively. Find the ∠BXY, ∠DYZ and ∠YZE.

Answer 1

Step-by-step explanation:

Let y and z be 3u and 7u

∠x=∠z (Alternate angles)

∠x+∠y=180

∘

(Angles made on same side of transversal)

Put x=z

∠z+∠y=180

∘

7u+3u=180

∘

10u=180

∘

u=

10

180

∘

=18

∘

z=7×18

∘

=126

∘

x=z=126

∘

Answer 2

Given:  AB || CD || EF intersected by a  transversal PQ at X, Y and Z respectively  ∠AXP = 8a , ∠FZY = 7a

To find : ∠BXY, ∠DYZ and ∠YZE.​

Solution:

∠BXY = ∠AXP  ( vertically opposite angle)

∠AXP = 8a

=> ∠BXY = 8a

∠BXZ  +   ∠FZP = 180°    ( angles created in between the parallel lines AB & EF)

∠BXZ  = ∠BXY = 8a

∠FZP  = 7a

=> 8a + 7a = 180°

=> 15a = 180°

=> a = 12°

∠BXY = 8a = 8 * 12 = 96°

∠BXY = 96°

∠DYZ = ∠FZP  = 7a = 84°

∠FZP  =  84°

∠YZE + ∠FZY  = 180°  Straight line

∠FZY = ∠FZP   = 84°

=> ∠YZE + 84° = 180°

=> ∠YZE = 96°

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