Question

a student uses the vertical angles theorem and the definition of complementary angles to conclude m∠ptr = 50 in the figure. what mistake did the student make? choose the correct answer below a. the student used the definition of complementary angles instead of the definition of vertical angles. b. the student used the definition of complementary angles instead of the definition of supplementary angles. c. the student used the definition of complementary angles instead of the definition of right angles. d. the student used the definition of vertical angles instead of the definition of right angles.

Explanation:

To solve this, we analyze the student's mistake. Vertical angles are equal, but complementary angles sum to \(90^\circ\), supplementary to \(180^\circ\), and right angles are \(90^\circ\). The student should have used the correct angle - related definition. Option B says the student used complementary (sum to \(90^\circ\)) instead of supplementary (sum to \(180^\circ\)) when dealing with angles formed by intersecting lines (where adjacent angles are supplementary).

Answer:

B. The student used the definition of complementary angles instead of the definition of supplementary angles.