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Find the angles given in the figure.
"
Given :
∠ABP = 35° and ∠QAB = 65°
To find :
We have to find the angles ∠PAB and ∠QBA.
Solution :
We know that,
Angle formed by the diameter on any point of the circle is 90°.
Therefore,
 ∠APB = 90° and ∠AQB = 90°
Sum of the angles in a triangle is 180°.
$ ∠APB +  ∠ABP +  ∠PAB = 180°$
$90°+35°+∠PAB = 180°$
$∠PAB = 180°-125°$
∠PAB = 55°
$∠AQB +  ∠ABQ +  ∠QAB = 180°$
$90°+65°+∠QBA = 180°$
$∠QBA = 180°-155°$
∠QBA = 25°.
Angels ∠PAB and ∠QBA are 55° and 25°.
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