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What is the sum of $∠ B A D + ∠ B P R + ∠ B C D + ∠ B Q R$ in the above figure?

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540 °

360 °

240 °

Angle Subtended by an Arc of a Circle of the above

answer is B.

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Detailed Solution

Given,

In cyclic quadrilateral

B A D C,

∠ B A D + ∠ B C D = 180 °

Since, the sum of the opposite angles of a cyclic quadrilateral is

180 °

.
In cyclic quadrilateral

B P R Q,

∠ B P R + ∠ B Q R = 180 °

We know that the sum of the opposite angles of a cyclic quadrilateral is

180 °

.
So,

∠ B A D + ∠ B P R + ∠ B C D + ∠ B Q R = 180 ° + 180 ° ⇒ ∠ B A D + ∠ B P R + ∠ B C D + ∠ B Q R = 360 °

Hence, the correct option is 2.

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