Q. 12

# 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.

Answer :

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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