In the given figure, 𝒑 || 𝒒 and 𝒍 and 𝒎 are transversals. The measures of some angles are shown below. Hence, find the measures of ∠𝒂, ∠𝒃, ∠𝒄 and ∠𝒅.

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Solution

Consider the parallel lines p and q and the transversal ‘m’.

∠d = 180° - 115° = 65° [linear pair axiom]
∠c = 115° [corresponding angles]

Now, we have to find the values of ‘a’ and ‘b’.
We should be considering the transversal ‘l’ to find the values of ‘a’ and ‘b’.

∠a = 180° – 110° = 70° [linear pair axiom]
∠b = ∠a = 70° [alternate exterior angles]

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