Question

Select the correct answer. The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m<ABC​

Answer 1

Answer:
`45^(\circ)`

Explanation:

`\angle ABC` is formed by
`\overline{AB}` and
`\overline{BC}`, so we can begin by finding their slopes.

`m_{\overline{AB}}=(2-5)/(4-7)=-1\\m_{\overline{BC}}=(2-2)/(9-4)=0`

This means that:

`\tan \left(\angle ABC \right)=\left| (-1-0)/(1-(0)(-1)) \right|\\\tan \left(\angle ABC \right)=1`

As
`\angle ABC` is acute, this means
`m\angle ABC=\boxed{45^(\circ)}`