1.

In the given figure, Line AB || line CD || line EF and line QP is their transversal. If y : z = 3 : 7 then find the measure of ∠x.

Answer»

y : z = 3 : 7 [Given] 

Let the common multiple be m 

∴ ∠j = 3m and ∠z = 7m ….(i) 

line AB || line EF and line PQ is their transversal 

[Given]

∠x = ∠z

∴ ∠x = 7m …..(ii) [From (i)] 

line AB || line CD and line PQ is their transversal 

[Given]

∠x + ∠y = 180° 

∴ 7m + 3m = 180° 

∴ 10m = 180°

∴ m = 18

∴ ∠x = 7m = 7(18°) [From (ii)] 

∴ ∠x = 126°



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