AB and CD are two chords in a circle with centre O and AD is the diameter. When produced, AB and CD meet at the point P. If ∠DAP = 27°, ∠APD = 35°, then what is the measure (in degrees) of ∠DBC?

28

\(\angle\)DAP = \({27}^\circ\)

\(\angle\)APD = \({35}^\circ\)

In \(\Delta \)ADP

⇒ \(\angle\)ADC = \({27}^\circ\) + \({35}^\circ\) = \({62}^\circ\)

⇒ \(\angle\)ABC = \(\angle\)ADC = \({62}^\circ\)  (angle formed by same arc)

⇒ \(\angle\)ABD = \({90}^\circ\) (angle formed by diameter in semi circle)

⇒ \(\angle\)DBC = \(\angle\)ABD - \(\angle\)ABC

⇒ \({90}^\circ\) - \({62}^\circ\) = \({28}^\circ\)

Therefore, the answer is \({28}^\circ\)