ABCD is a cyclic quadrilateral whose diagonals intersect at P. If AB = BC, ∠DBC = 70° and ∠BAC = 30°, then the measure of ∠PCD is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 50°
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Concept |
Understanding |
Application |
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In a cyclic quadrilateral, opposite angles are supplementary angles. Angles made by the same cord of a circle are equal. |
Given: AB = BC, ∠DBC = 70° and ∠BAC = 30°
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Since AB = BC So, ∠BAC = ∠BCA = 30° And ∠DBC = ∠DAC = 70° (Angles made by same cord CD) ∠BAD +∠BCD = 180° 100° + ∠BCD = 180° ∠ BCD = 80° So, angle ∠PCD = 80 – 30 = 50° |
