Question

question 12 (multiple choice worth 4 points) (01.06r lc) angles bae and fac are straight angles. what angle relationship best describes angles bac and eaf? adjacent angles complementary angles supplementary angles vertical angles

Explanation:

Step1: Recall angle - relationship definitions

Adjacent angles share a common side and a common vertex. Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. Vertical angles are opposite each other when two lines intersect.

Step2: Analyze the given angles

Since angles BAE and FAC are straight angles (180 degrees), and \(\angle BAE=\angle BAC+\angle CAE\) and \(\angle FAC = \angle FAE+\angle CAE\). We know that \(\angle BAC+\angle CAE = 180^{\circ}\) and \(\angle FAE+\angle CAE=180^{\circ}\), so \(\angle BAC=\angle FAE\) (by subtracting \(\angle CAE\) from both equations). Vertical angles are formed by the intersection of two lines and are equal. Angles BAC and EAF are opposite each other when the lines intersect at point A.

Answer:

D. Vertical angles