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In the figure given below, if PQ||AB and PR||BC are such that $∠ Q P R = 102 °,$ then what is the measure of the $∠ A B C$ then what is the measure of the ?

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78 °

100 °

40 °

30 °

answer is A.

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Detailed Solution

It is given that PQ||AB and PR||BC such that

∠ Q P R = 102 ° .

Expand the line BA to meet the line PR at E as shown in the figure given below.
Question Image

Since the lines BA || QP, and PR is a transversal, therefore, using the interior angle property, we have,

∠ Q P R + ∠ P E B = 180 °

⇒ ∠ P E B = 180 ° − 102 ° [∵ ∠ Q P R = 102 °]

⇒ ∠ P E B = 78 °

Using the alternate interior angle property, we have,

∠ A B C = ∠ P E B = 78 ° ⇒ ∠ A B C = 78 °

Therefore, the measure of the angle

∠ A B C = 78 ° .

Hence, option (1) is correct.

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