2023 AMC 12A Problem 11

Problem 11 of 25IntermediateGeometry

What is the degree measure of the acute angle formed by lines with slopes

2

and

\tfrac13?

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Solution

The tangent of the angle between the lines is

\left|\dfrac{2-\tfrac13}{1+2\cdot\tfrac13}\right| =\left|\dfrac{\tfrac53}{\tfrac53}\right|=1.

The acute angle with tangent

1

45^\circ.

Thus, the correct answer is C.

Concepts: slope · trigonometry

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