Question:
In figure, if AOB is a diameter and ∠ADC = 120°, then ∠CAB = 30°.
Solution:
True
Join CA and CB.
Since, ADCB is a cyclic quadrilateral.
∠ADC + ∠CBA = 180°.
[sum of opposite angles of cyclic quadrilateral is 180°]
=>∠CBA = 180° -120° = 60° [∴ ∠ADC = 120°]
In ΔACB, ∠CAB + ∠CBA + ∠ACB = 180°
[by angle sum property of a triangle]
∠CAB + 60°+ 90°= 180°
[triangle formed from diameter to the circle is 90° i.e., ∠ACB = 90°)
=> ∠CAB = 180° – 150° = 30°.