1. **Problem Statement:** Given two parallel lines L1 and L2 intersected by two transversals t1 and t2, find the measures of angles 1, 2, 3, and 4 using the given angles 109° and 87° and the properties of parallel lines and transversals. 2. **Relevant Rules and Formulas:** - Corresponding angles are equal when two parallel lines are cut by a transversal. - Alternate interior angles are equal. - Supplementary angles add up to 180°. 3. **Step-by-step Solution:** **Angle 1:** - Angle 1 is at the intersection of L2 and t1, top-right. - Given angle adjacent to angle 1 is 109°. - Since angles on a straight line sum to 180°, $$\angle 1 + 109^\circ = 180^\circ$$ - Subtracting 109° from both sides: $$\angle 1 = 180^\circ - 109^\circ = 71^\circ$$ **Angle 2:** - Angle 2 is at the intersection of L1 and t1, bottom-left. - By the Corresponding Angles Postulate, angle 2 corresponds to angle 1 because L1 and L2 are parallel and t1 is a transversal. - Therefore, $$\angle 2 = \angle 1 = 71^\circ$$ **Angle 3:** - Angle 3 is at the intersection of L2 and t2, left side. - Given angle adjacent to angle 3 is 87°. - Angles on a straight line sum to 180°, so $$\angle 3 + 87^\circ = 180^\circ$$ - Subtracting 87° from both sides: $$\angle 3 = 180^\circ - 87^\circ = 93^\circ$$ **Angle 4:** - Angle 4 is at the intersection of L1 and t2, above the lower line. - By Corresponding Angles Postulate, angle 4 corresponds to angle 3. - Therefore, $$\angle 4 = \angle 3 = 93^\circ$$ 4. **Final answers:** - $$\angle 1 = 71^\circ$$ - $$\angle 2 = 71^\circ$$ - $$\angle 3 = 93^\circ$$ - $$\angle 4 = 93^\circ$$