Final answer:
Option A) m25 + m22 + m26 = 180° This demonstrates the application of the corresponding angles postulate and the linear pair postulate in proving the sum of angles when two lines are parallel and a transversal intersects them.
Step-by-step explanation:
Given that y || z, we can use the corresponding angles postulate. When a transversal intersects two parallel lines, corresponding angles are congruent. Hence, m25 and m22 are congruent due to their corresponding positions. Also, m26 and m22 are supplementary angles because they form a linear pair, sharing a common side and forming a straight line. So, m25 + m22 + m26 equals 180°, representing the sum of the measures of angles in a straight line.
The angles m25 and m22 are congruent because they are corresponding angles formed by the parallel lines and the transversal. As y || z, m25 is congruent to m22. Meanwhile, m26 and m22 together form a linear pair, as they share a common side and together form a straight line. According to the linear pair postulate, the sum of the measures of two supplementary angles is 180°. Therefore, combining m25, m22, and m26 gives the total measure of 180°, verifying Option A as the correct answer.
This demonstrates the application of the corresponding angles postulate and the linear pair postulate in proving the sum of angles when two lines are parallel and a transversal intersects them.