1. **Problem Statement:** Given two parallel lines $l_1$ and $l_2$ cut by a transversal, find the measures of the indicated angles $\angle 3$ and $\angle 5$ given that $\angle 1 = 68^\circ$, $\angle 2 = 68^\circ$, and $\angle 4 = 120^\circ$. 2. **Important Rules:** - Corresponding angles formed by a transversal with parallel lines are equal. - Alternate interior angles are equal. - The sum of angles on a straight line is $180^\circ$. 3. **Given:** $$\angle 1 = 68^\circ, \quad \angle 2 = 68^\circ, \quad \angle 4 = 120^\circ$$ 4. **Find $\angle 3$: ** Since $\angle 3$ and $\angle 4$ are supplementary (they form a linear pair on the transversal), $$\angle 3 + \angle 4 = 180^\circ$$ Substitute $\angle 4 = 120^\circ$: $$\angle 3 + 120^\circ = 180^\circ$$ $$\angle 3 = 180^\circ - 120^\circ = 60^\circ$$ 5. **Find $\angle 5$: ** $\angle 5$ corresponds to $\angle 1$ because they are corresponding angles formed by the transversal cutting parallel lines $l_1$ and $l_2$. Therefore, $$\angle 5 = \angle 1 = 68^\circ$$ **Final answers:** $$\angle 3 = 60^\circ, \quad \angle 5 = 68^\circ$$