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

User Zayn Ali
by
3.0k points

1 Answer

18 votes
18 votes

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)}

Select the correct answer. The vertices of a triangle are A(7, 5), B(4, 2), and C-example-1
Select the correct answer. The vertices of a triangle are A(7, 5), B(4, 2), and C-example-2
User William Linton
by
3.2k points