Q10 of 100 Page 17

In a cyclic quadrilateral ABCD, if m ∠A =3(m∠C). Find m∠A.

WE have,

∠A = 3 ∠C

Let, ∠C = x

Therefore,

∠A + ∠C = 180^o (Opposite angles of cyclic quadrilateral)

3x + x = 180^o

4x = 180^o

x = 45^o

∠A = 3x

= 3 * 45^o

= 135^o

Therefore,

∠A = 135^o

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

In a cyclic quadrilateral ABCD if AB||CD and B=70°, find the remaining angles.

In Fig. 16.183, O is the centre of the circle ∠DAB=50°. Calculate the values of x and y.

In Fig. 16.184, if ∠BAC=60° and ∠BCA=20°, find ∠ADC.