Question

which statement justifies why ∠abf measures 130°? given: angles abd and dbc are complementary a linear pair is two adjacent, supplementary angles. the sum of the measures of complementary angles is 90 degrees. if two angles are vertical angles, then they are congruent. alternate interior angles are congruent

Explanation:

Step1: Identify angle - relationship

We know that \(\angle ABD = 50^{\circ}\) and we want to find \(\angle ABF\). \(\angle ABD\) and \(\angle ABF\) form a linear - pair.

Step2: Recall linear - pair property

A linear pair is two adjacent, supplementary angles. That is, if two angles form a linear pair, the sum of their measures is \(180^{\circ}\). Let \(m\angle ABD=x = 50^{\circ}\) and \(m\angle ABF = y\). Then \(x + y=180^{\circ}\).

Step3: Calculate \(\angle ABF\) measure

Substitute \(x = 50^{\circ}\) into \(x + y=180^{\circ}\), we get \(y=180^{\circ}-50^{\circ}=130^{\circ}\).

Answer:

A linear pair is two adjacent, supplementary angles.