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

It is given that, AB  as diameter, O  is centre and`angle CAB = 30°`   

We have to find `m  angleACB` and ` m  angleABC`

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

`angleACB = 90°`

In Δ ACD  we have

`angleCAB` = 30° (Given)

  `angleACB `= 90°  (Angle in semi-circle is right angle)

Now in Δ ACB   we have

`angleCAB  +  angleACB  + angleABC  `= 180

                    `angleABC = 180° - (angle CAB + angleCAB )`

                                       =180° - (90° + 30° ) 

                                      = 180° - 120° 

                                       = 60°

                             

Hence `angle ABC = 60°` and `angleACB = 90°`