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Problem 359: (2023 AMC12A, 11)
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exercises solutions
Problem 359: (2023 AMC12A, 11)
What is the degree measure of the acute angle formed by lines with slopes $2$ and $\tfrac{1}{3}$? $\textbf{(A)}~30\qquad$ $\textbf{(B)}~37.5\qquad$ $\textbf{(C)}~45\qquad$ $\textbf{(D)}~52.5\qquad$ $\textbf{(E)}~60$
Solution
$\tan\theta=\left|\dfrac{2-\frac13}{1+\frac23}\right|=\left|\dfrac{5/3}{5/3}\right|=1$.
$\theta=45^\circ$, answer
(C)
.
Exercise 359:
Solution
What is the degree (or radian) measure of the acute angle formed by lines with slopes $3$ and $\frac14$?
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