AB is the diameter of a circle with centre O. C and D are two points on the circle on either side of AB, such that ∠ CAB = 52° and ∠ ABD = 47° What is the difference (in degrees) between the measures of ∠ CAD and ∠ CBD ?

10

According to the concept,

\(\angle\)ACB = \(\angle\)ADB = \({90}^\circ\)

So, \(\angle\)CBA = \({180}^\circ\) - (\({90}^\circ\) + \({52}^\circ\))

⇒ \({180}^\circ\) - \({142}^\circ\)

⇒ \({38}^\circ\)

Similarly,

⇒ \(\angle\)BAD = \({180}^\circ\) - (\({90}^\circ\) + \({47}^\circ\))

⇒ \({180}^\circ\) - \({137}^\circ\)

⇒ \({43}^\circ\)

So, \(\angle\)CAD = \({52}^\circ\) + \({43}^\circ\)

⇒ \({95}^\circ\)

\(\angle\)CBD = \({38}^\circ\) + \({47}^\circ\)

⇒ \({85}^\circ\)

Now,

\(\angle\)CAD - \(\angle\)CBD = \({95}^\circ\) - \({85}^\circ\)

⇒ \({10}^\circ\)

Therefore, the difference between the measures of ∠ CAD and ∠ CBD is \({10}^\circ\)