Q8 of 45 Page 164

In the adjoining figure, and are parallel lines. The transversals and intersect at U on the line . Given that ∠DWU = 110° and ∠CVP = 70°, find the measure of ∠QUS.

We know, ∠CVP = 70°,


∴∠UVW = 70° [∵ Vertically opposite angles]


Again,


⇒ ∠UWV + ∠DWU = 180°


⇒ ∠UWV = 180° - 110°


⇒ ∠UWV = 70°


In ΔUVW,


⇒ ∠UVW + ∠UWV + ∠VUW = 180°


⇒ 70° + 70° + ∠VUW = 180°


⇒ ∠VUW = 180° - 140° = 40°


∴ ∠QUS = ∠VUW = 40° [Vertically opposite angle]


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