In the figure 5.70 given below AC||PQ and AB || RS then find the value of ∠y. Give the reasons of the statements to be used in the solution.
From the figure above it can be clearly seen that,
∠BDS + ∠SDC = 180° [ Angles made on straight line]
∠BDS + 80° = 180°
∠ BDS = 100°
Now, ∠ABC = ∠BDS = 100° [Alternate angles are equal]
Now from triangle ABC
Sum of interior angles of a triangle = 180°
∠ABC + ∠ACB + ∠BAC = 180°
100° + 30° + ∠BAC = 180°
∠BAC = 50°
Y = ∠BAC = 50°
As AC || PQ and thus alternate angles are equal.
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