Using the cosine rule formula to solve for angle O
[tex]\begin{gathered} 12^2=20^2+20^2-2(20)(20)cosO \\ \end{gathered}[/tex]
Solve for angle O
[tex]\begin{gathered} 144=400+400-800cosO \\ 800cosO=800-144 \\ cosO=\frac{656}{800}=0.82 \\ O=\cos^{-1}(0.82)=34.92^{\circ\:} \\ \therefore O=34.92^0 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} \angle AOC=2\angle ABC \\ \therefore\angle ABC=\frac{\angle AOC}{2}=\frac{34.92}{2}=17.46^0 \end{gathered}[/tex]
Hence, the answer is
[tex]\angle ABC=17.46^0[/tex]
