Question

in the picture, one angle is labeled 22° and lines s and t are parallel. which other three angles will be 22°? separate each angle number with a comma. (1 point) angles

Explanation:

Step1: Use alternate interior angles

Since lines \(S\) and \(T\) are parallel, angle \(3\) and the \(22^{\circ}\) angle are alternate - interior angles. So, \(\angle3 = 22^{\circ}\).

Step2: Use vertical angles

Vertical angles are equal. \(\angle3\) and \(\angle6\) are vertical angles. So, \(\angle6=\angle3 = 22^{\circ}\). Also, \(\angle3\) and \(\angle1\) are supplementary (\(\angle1+\angle3 = 180^{\circ}\)), but \(\angle2\) and \(\angle3\) are vertical angles (if we consider the intersection on line \(S\)). Wait, no. Let's re - check.
Since \(\angle3 = 22^{\circ}\), and \(\angle3\) and \(\angle2\) are vertical angles (at the intersection on line \(S\)), \(\angle2=\angle3 = 22^{\circ}\) (vertical angles). Also, \(\angle3\) and \(\angle6\) are alternate - exterior angles (another way: \(\angle5=180 - 22=158^{\circ}\) (linear pair with \(22^{\circ}\) angle on line \(T\)), \(\angle7 = 158^{\circ}\) (vertical angles with \(\angle5\)), \(\angle6=22^{\circ}\) (linear pair with \(\angle5\))

Answer:

\(2,3,6\)