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In this, how are $\measuredangle PAD$ and $\measuredangle DBA$ equal?

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1 Answer 1

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They are equal by alternate segment theorem:

"The alternate segment theorem states that in any circle, the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment."

enter image description here

In this picture, the angles which are the same colour are equal. Applying this to your diagram, we can see that $\measuredangle PAD = \measuredangle DBA$

Do you require a proof?

Edit (proof):

enter image description here

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