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Triangle and Sum of Its Internal Angles

In the given ...

Question

In the given figure, BC || AD. Find the value of x and y.

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Solution

We have, BC || AD and CD is the transversal
Thus, ∠BCD and ∠ADP are corresponding angles
∴ ∠BCD = ∠ADP
⇒ y = 100^∘
Also, ∠ADC and ∠ADP form a linear pair
∴ ∠ADC + ∠ADP = 180^∘
⇒ x + 100^∘= 180^∘
⇒ x = 180^∘ − 100^∘
= 80^∘
Thus, x = 80^∘ and y = 100^∘

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