Question

Find the angles x and y in the figure. $AO=OB$

Answer 1

Since,

$AO=OB\Rightarrow \angle ABO=\angle x..........\left(1\right)$

Now, $\angle AOB={92}^o$ as it is vertically oppsite angle to ${92}^o$

Also, According to Sum of Opposite angle Rule

$x+{92}^o=y...................\left(2\right)$

Also, $\angle ABO+y={180}^o\Rightarrow \angle ABO={180}^o-y...................\left(3\right)$

From (1),(2) and (3)

$x={180}^o-y\Rightarrow x={180}^o-(x+{92}^o)\Rightarrow 2x={88}^o\Rightarrow x={44}^o$

$y={180}^o-x={180}^o-{44}^o={136}^0$