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Problem 485

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

4. Given that $\alpha-l-\beta$ is a right dihedral angle, $A \in \alpha, B \in \beta, A, B$ are not on $l$ , and let the angles formed by $AB$ with $\alpha$ and $\beta$ be $\theta_{1}$ and $\theta_{2}$ , respectively, then the range of $\theta_{1}+\theta_{2}$ is $\qquad$ -

Your answer

Official solution

$\left(0, \frac{\pi}{2}\right)$ ;

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.