Final Answer:
Lines b and c are parallel. What is the measure of angle 26 is 117° (option c)
Step-by-step explanation:
When two lines are parallel and intersected by a transversal, alternate interior angles are congruent. In this case, angle 26 is an alternate interior angle with angle 117°. (option c)
Therefore, the measure of angle 26 is also 117°. This property is based on the relationship between parallel lines and the angles formed when a transversal intersects them, resulting in congruent alternate interior angles.
The concept of alternate interior angles relies on the parallel lines and transversal relationship, where these angles lie on opposite sides of the transversal but between the parallel lines. This property holds true regardless of the orientation or positioning of the lines.
Understanding angle relationships formed by intersecting lines, especially when dealing with parallel lines and transversals, is crucial in geometry. Properties like alternate interior angles play a significant role in proving the congruence of angles and solving geometric problems involving parallel lines.