Question

Find $x$, for the following diagram:

Answer 1

We know that angles in same segment are equal
$\angle ADB$ and $\angle ACB$ are angles of same segment
Thus, $\angle ACB=\angle ADB$ $[\because \angle ADB={30}^0]$ (given)
$\angle ACB={30}^0$ ……(i)
Angle of same segment are equal .
$\angle ACD$ and $\angle DBA$ are angles of same segment.
$\angle ACD=\angle DBA$
$\angle ACD={60}^0$ $[\because \angle DBA={60}^0]$ …..(ii)
$x=\angle ACB+\angle ACD$
From equation (i) and (ii)
$x={30}^0+{60}^0$
$x={90}^0$.