Question

ABCD is a cyclic-quadrilateral whose centre is O and AB is diameter. If angle BAC = 30°, then angle ADC is?​

Answer 1

Answer:

∠ADC+∠ABC=180 °

....(since the sum of the opposite angles of a quadrilateral is 180 ° ).

∴∠ABC=180 ° -30° =150°.

Also, ∠ACB=90° ....(since the angle subtended by a diameter at the circumference of the circle, is 90 o ).

∴ In ΔABC we have,∠ACB=90°and ∠ABC=150°

So, ∠CAB=180 ° −(∠ACB+∠ABC)

=180 °−(90 °+150°)

∴∠BAC=160°