Q12 of 32 Page 67

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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