Parallel Lines

Concept: When a transversal intersects two parallel lines, specific relationships exist between the angles formed. Interior angles on the same side of the transversal are supplementary (their sum is ). These are also known as consecutive interior angles or same-side interior angles. Step 1: Understand the property of consecutive interior angles If two parallel lines are intersected by a transversal, then the sum of the interior angles on the same side of the transversal is . Let the two consecutive interior angles be and . If the lines are parallel, then . Step 2: Set up the angles based on the given ratio The two interior angles are in the ratio 2 : 3. Let the common factor for the ratio be . Then the measures of the two angles are and . Step 3: Use the supplementary property to form an equation Since these are consecutive interior angles and the lines are parallel, their sum must be : Step 4: Solve for Step 5: Calculate the measures of the two angles The first angle is . The second angle is . Step 6: Identify the larger angle Comparing the two angles, and , the larger angle is . (Check: , so they are supplementary). The measure of the larger angle is .