Question: 21. In the figure below, line \( r \) is parallel to line \( s \), and line \( u \) is…

21. In the figure below, line \( r \) is parallel to line \( s \), and line \( u \) is perpendicular to line \( t \).

Suppose the \( m \angle 1 = 60^\circ \). Find the \( m \angle 5 \).

[Diagram of lines \( r \), \( s \), \( t \), and \( u \) with angles labeled 1 to 10]

Your answer

Solution

To find the measure of \(\angle 3\), let’s use the given information and properties of angles. 1. Since \(r\) is parallel to \(s\) and \(t\) is a transversal, \(\angle 1\) and \(\angle 5\) are corresponding angles. 2. Therefore, \(\angle 1 = \angle 5 = 60^\circ\). 3. Since \(u\) is perpendicular to \(t\), \(\angle 5 + \angle 3 = 90^\circ\). 4. Substitute \(\angle 5 = 60^\circ\) into the equation: \[ 60^\circ + \angle 3 = 90^\circ \] 5. Solve for \(\angle 3\): \[ \angle 3 = 90^\circ - 60^\circ \] 6. Therefore, \(\angle 3 = 30^\circ\).