Question

in the given figure, O is the centre of the circle and angle DAB =50°. Find x and y.

Answer 1

I hope you were looking for my answer

Answer 2

Given:

O is the centre of the circle and angle DAB =50°.

To find:

The values of x and y.

Solution:

In triangle OAB,

$OA = OB$        (Radii of same circle)

So, triangle OAB is an isosceles triangle.

$\angle OAB=\angle OBA=50^\circ$          (Base angles of an isosceles triangle)

Now,

$\angle BOD=\angle OAB+\angle OBA$    (Exterior angle theorem)

$x=50^\circ+50^\circ$

$x=100^\circ$

Now,

$reflex\angle BOD=360^\circ-100^\circ$

$reflex\angle BOD=260^\circ$

$\angle BCD=\dfrac{reflex\angle BOD}{2}$       (Central angle theorem)

$y=\dfrac{260^\circ}{2}$

$y=130^\circ$

Therefore, the value of x is 100° and the value of y is 130°.