$\begin{align}(i)30+90+x=&180\\[5pt] 120+x=&180\\[5pt] x=&180-120\\[5pt] &\underline{\underline{60^0}}\\ \end{align}$	$\begin{align}(ii)x+x+90=&180\\[5pt] 2x+90=&180\\[5pt] 2x=&90\\[5pt] &\underline{\underline{45^0}}\\ \end{align}$	$\begin{align}(iii)y+60+90=&180\\[5pt] y+150=&180\\[5pt] y=&180-150\\[5pt] &\underline{\underline{30^0}}\\ 90+x+y=&180\\[5pt] 90+x+30=&180\\[5pt] x=&180-120\\[5pt] &\underline{\underline{x=60^0}}\\ \end{align}$
$\begin{align}(iv)x+50+90=&180\\[5pt] x+140=&180\\[5pt] x=&180-140\\[5pt] &\underline{\underline{40^0}}\\ \end{align}$	$\begin{align}(v)x+90+90+110=&360\\[5pt] x+290=&360\\[5pt] x=&360-290\\[5pt] &\underline{\underline{70^0}}\\ \end{align}$

By studying this lesson you will be able to

Identify and apply the theorems related to angles in a circle.