Question

in the given figure ABCD is a cyclic quadrilateral with side AB as the diameter of the circle.
if ∠ADC=110°, find the measure of
i) ∠ABC
ii) ∠CAB​

Answer 1

Answer:

∠ACB=90° (angle subtended by the diameter of circle)

and ∠ABC is the supplementary angle of ∠ADC...(opposite angles of cyclic quadrilateral)

∴∠ABC=180°−∠ADC=180°−130°=50°

Now, by angle sum property,

∠BAC=180°−(∠ACB+∠ABC)

=180°−50°−90°=40°