Equations with Angles from Parallel Lines Cut by a Transversal--Example 10

Topic

Equations

Description

This final example in the series focuses again on same side interior angles in parallel lines cut by a transversal. The diagram shows two parallel lines intersected by a transversal, with one same side interior angle measuring 123° and the other labeled x°. The angle vertical to the 123° forms a pair of same side interior angles with x. As we've seen in previous examples, same side interior angles are supplementary when the lines are parallel. To solve for x, we set up the equation: 123 + x = 180. Subtracting 123 from both sides yields x = 57. This example reinforces the consistent relationship between same side interior angles in parallel line configurations. It's worth noting that this property can also be used to prove that two lines are parallel if the same side interior angles are supplementary. By working through multiple examples with different angle measures, students can develop a deeper understanding of the geometric principles at play and their algebraic representations. This series of examples demonstrates the interconnectedness of various angle relationships in parallel line configurations and how they can be used to solve for unknown angles.

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