Answer: [tex]45^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle ABC[/tex] is formed by [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex], so we can begin by finding their slopes.
[tex]m_{\overline{AB}}=\frac{2-5}{4-7}=-1\\m_{\overline{BC}}=\frac{2-2}{9-4}=0[/tex]
This means that:
[tex]\tan \left(\angle ABC \right)=\left| \frac{-1-0}{1-(0)(-1)} \right|\\\tan \left(\angle ABC \right)=1[/tex]
As [tex]\angle ABC[/tex] is acute, this means [tex]m\angle ABC=\boxed{45^{\circ}}[/tex]
