Question

question 14 (1 point)
(01.06 mc)
given: angles abd and dbc are complementary
which statement justifies why ∠ebc measures 90°?
○ a a linear pair is two adjacent, supplementary angles.
○ b the sum of the measures of complementary angles is 90 degrees.
○ c if two angles are vertical angles, then they are congruent.
○ d alternate interior angles are congruent.

Explanation:

• Option a: A linear pair being two adjacent, supplementary angles is about angles summing to \(180^{\circ}\), not relevant to \(\angle EBC = 90^{\circ}\).
• Option b: Since \(\angle ABD\) and \(\angle DBC\) are complementary (sum to \(90^{\circ}\)), and \(\angle ABE\) is a straight - line angle (\(180^{\circ}\)). We know that \(\angle EBC=180^{\circ}-\angle ABD - \angle DBC\). Given \(\angle ABD+\angle DBC = 90^{\circ}\) (complementary angles definition: sum of complementary angles is \(90^{\circ}\)), then \(\angle EBC = 90^{\circ}\).
• Option c: Vertical angles congruence is about angles opposite each other when two lines intersect, not relevant to this angle - sum situation.
• Option d: Alternate interior angles congruence is a property in parallel - line and transversal set - ups, not applicable here.

Answer:

B. The sum of the measures of complementary angles is 90 degrees.