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.

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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