Mathematics

The key is recognizing that $\cos 2\theta$ gives you information about the double angle, so you'll need to work backwards to find $\theta$ itself. Since $\theta$ is obtuse (between 90° and 180°), that means $2\theta$ falls in a specific range where you can pin down which quadrant it's in and thus which inverse cosine value to use. Use the relationship between $\cos 2\theta$ and the angle $2\theta$ to find the actual measure, then divide by 2.

The key is recognizing that $\cos 2\theta$ gives you information about the double angle, so you'll need to work backwards to find $\theta$ itself. Since $\theta$ is obtuse (between 90° and 180°), that means $2\theta$ falls in a specific range where you can pin down which quadrant it's in and thus which inverse cosine value to use. Use the relationship between $\cos 2\theta$ and the angle $2\theta$ to find the actual measure, then divide by 2.