In the adjoining figure, ↔AB and ↔CD are parallel lines. The transversals ↔PQ and ↔RS intersect at U on the line ↔AB. Given that ∠DWU=110o and ∠CVP=70o, find the measure of ∠QUS.
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Solution
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Given ∠CVP=70o and ∠DWU=110o
∴∠CVP=∠UVW=70o [Alternate Angle]
∠UWD+∠DWR=180o [Adjacent Angle]
∴∠DWR=180o−110o=70o
∠DWR=∠UWV=70o [Alternate angles]
Consider △UVW
By angle sum property,
∠VUW+70+70=180o
⇒∠VUW=40o
∠VUW=∠QUS=40o ...... [Vertical Opposite Angles]
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