Science:Math Exam Resources/Courses/MATH152/April 2022/Question A18/Statement

Let ${\textstyle {\mathit {Ref}}_{\alpha }}$ be the reflection of the plane ${\textstyle \mathbb {R} ^{2}}$ across the line ${\textstyle L}$ that makes an angle ${\textstyle \alpha }$ with the positive ${\textstyle x_{1}}$-axis. The composition of two such reflections

$${\mathit {Ref}}_{50^{\circ }}\circ {\mathit {Ref}}_{30^{\circ }}$$

is the rotation by an angle ${\textstyle \theta }$. Find this ${\textstyle \theta }$.