Question

5 which theorem would be used to write 15x + 12 + 117 = 180 in the diagram below?
corresponding angles theorem
consecutive exterior angles theorem
alternate interior angles theorem
vertical angles theorem

Explanation:

• Corresponding Angles Theorem: States that if two parallel lines are cut by a transversal, then each pair of corresponding angles is equal. This does not apply here as the equation \(15x + 12+117 = 180\) is about supplementary angles, not equal angles.
• Consecutive Exterior Angles Theorem: When two parallel lines are cut by a transversal, consecutive exterior angles are supplementary (their sum is \(180^{\circ}\)). In the given diagram, assuming lines \(k\) and \(j\) are parallel and cut by transversal \(l\), \(15x + 12\) and \(117^{\circ}\) are consecutive exterior angles. So, their sum \(15x + 12+117 = 180\) is based on this theorem.
• Alternate Interior Angles Theorem: States that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is equal. This is not relevant to the sum - to - \(180^{\circ}\) equation.
• Vertical Angles Theorem: States that vertical angles (opposite angles formed by two intersecting lines) are equal. This has no relation to the sum \(15x + 12+117 = 180\).

Answer:

Consecutive Exterior Angles Theorem