Question

In the given figure ABCD is a cyclic quadrilateral with side AB as a diameter of the circle (2) If ∠ADC = 125°, then find the measure of the following angles, giving reasons​

Answer 1

Answer:

Given:

ABCD is a cyclic quadrilateral with AB as the diameter of the circle.

Also, ∠ADC=140

We have to find: ∠BAC.

Then,

∠ADC+∠ABC=180

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

∴∠ABC=180 −140 =40

Also, ∠ACB=90

....(since the angle subtended by a diameter at the circumference of the circle, is 90

∴ In ΔABC we have,

∠ACB=90 and ∠ABC=40

So, ∠CAB=180 −(∠ACB+∠ABC)=180 −(90 +40 )

∴∠BAC=50