Question

Please answer urgently

the given figure shows two intersecting circles if abc is 75 then the measure is pad is

Answer 1

Answer:

The answer is 125.

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Answer 2

Given,

Refer figure, ∠ABC = 75°.

To find,

∠PAD.

Solution,

From the given figure, it can be seen that PBCQ and APQD are two cyclic quadrilaterals in the two given circles.

In a cyclic quadrilateral, we know that the sum of the opposite angles is 180°.

So, in the cyclic quadrilateral PBCQ, we have,

∠PBC + ∠PQC = 180°.

⇒ ∠PQC = 180 - 75

⇒ ∠PQC = 105°.

Now, ∠PQC and ∠PQD make a linear pair. So,

∠PQC + ∠PQD = 180°.

⇒ ∠PQD = 180 - 105

⇒ ∠PQD = 75°.

Now, since APQD is also a cyclic quadrilateral, again, the sum of opposite angles will be 180°. Thus,

∠PAD + ∠PQD = 180°

∠PAD = 180 - 75

∠PAD = 105°.

Therefore, for the given figure, the measure of ∠PAD is 105°.