1. Given: \(\angle 1\) and \(\angle 2\) form a linear pair, \(\angle 2\) and \(\angle 3\) form a linear pair. 2. Write the equations for the linear pairs: \[m\angle 1 + m\angle 2 = 180^\circ\] 3. \[m\angle 2 + m\angle 3 = 180^\circ\] 4. Set the two expressions equal since both equal 180°: \[m\angle 1 + m\angle 2 = m\angle 2 + m\angle 3\] 5. Subtract \(m\angle 2\) from both sides: \[\cancel{m\angle 1} + \cancel{m\angle 2} - \cancel{m\angle 2} = \cancel{m\angle 2} + m\angle 3 - \cancel{m\angle 2}\] which simplifies to \[m\angle 1 = m\angle 3\] This proves that \(m\angle 1 = m\angle 3\) because they are vertical angles formed by the intersection of lines \(j\) and \(k\).