Question

On a semi-circle with AB as diameter, a point C is taken, so that m(∠CAB)= 30°. Find m(∠ACB) and m(∠ABC).

Answer 1

m(∠ACB) = 90° and m(∠ABC) = 60°.

Step-by-step explanation:

Given:

Here  AB as diameter.

m(∠CAB)= 30°.

Center is given as point O.

Since angle in a semi-circle is a right angle therefore

m(∠ACB) = 90°

In ΔACD, we have

m(∠CAB)= 30°             (Given)

 m(∠ACB) = 90°             (Angle in semi-circle is right angle)

Now in ΔACB, we have

m(∠CAB) + m(∠ACB) + m(∠ABC) = 180°

30° + 90° + m(∠ABC) = 180°

 m(∠ABC) = 180° -120

 m(∠ABC) = 60°

Therefore  m(∠ACB) = 90° and m(∠ABC) = 60°.