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2023 AMC 12A Problem 11

Problem 11 of 25IntermediateAlgebraGeometry

What is the degree measure of the acute angle formed by lines with slopes 22 and 13?\tfrac13?

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Solution

The tangent of the angle between the lines is ∣2−131+2⋅13∣=∣5353∣=1. \left|\dfrac{2-\tfrac13}{1+2\cdot\tfrac13}\right| =\left|\dfrac{\tfrac53}{\tfrac53}\right|=1. The acute angle with tangent 11 is 45∘.45^\circ. Thus, the correct answer is C.
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