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 ?
Answer & explanation
Correct answer: option 1
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 \({10}^\circ\)