2023 AMC 12A Problem 11

Below is the professionally curated solution for Problem 11 of the 2023 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 12A solutions, or check the answer key.

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Concepts:slopetrigonometry

Difficulty rating: 1570

11.

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

3030

37.537.5

4545

52.552.5

6060

Solution:

The tangent of the angle between the lines is 2131+213=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.

Problem 11 in Other Years