SSC CHSL 2021 PYQ — Question 51

The correct answer is option 3 i.e. 24°

Given:

AD is diameter.

 $\angle$DAP = 36° and $\angle$APC = 30°

Concept Used:

Exterior angle of a triangle = Sum of the two opposite interior angles of the triangle.

Angles in the same segment are equal.

Explanation:

According to the given question,

Now, in triangle ADP, 

$\angle$ADC = $\angle$DAP + $\angle$APD   ($\angle$ADC is exterior angle)

⇒ $\angle$ADC = 36° + 30° 

⇒ $\angle$ADC = 66°

Now, $\angle$ADC = $\angle$ABC = 66°   (Angles in the same segment)

Since AD is diameter, $\angle$ABD = 90°

So, $\angle$CBD = $\angle$ABD - $\angle$ABC = 90° - 66° = 24°

Hence the requied answer is 24°.