Question

The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m∠ ∠ A B C ?

Answer 1

Answer:
`45^(\circ)`

Explanation:

`\angle ABC` is formed by lines AB and BC.

• The slope of AB is
  `(2-5)/(4-7)=-1`

• The slope of BC is
  `(2-2)/(9-4)=0`.

This means

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

From the diagram, we can tell that angle ABC is acute, so it measures
`\boxed{45^(\circ)}`