The figure below shows two lines that intersect at point

Question

along with ray

. The angles are labeled 1 through 5.

Line A-B intersects on line C-D at E and forms the angles A-E-D labeled as 2, A-E-C labeled as 1, and D-E-B labeled 3. Ray E-F is perpendicular to the line C-D and forms the angles B-E-F labeled as 4 and right-angle F-E-C labeled as 5.

Which of the following statements are true? Select two that apply.

A.

Angle 2 and angle 5 are complementary angles.

B.

Angle 4 and angle 5 are adjacent angles.

C.

Angle 2 and angle 3 are supplementary angles.

D.

Angle 1 and angle 4 are vertical angles.

E.

Angle 1 and angle 5 are supplementary angles.

Answer 1

We can analyze the angles based on their relationships:

1. Angle 2 and angle 5: Angle 2 (A-E-D) and angle 5 (the right angle formed by ray E-F and line C-D) are not complementary. They are not angles that add up to 90 degrees together.

2. Angle 4 and angle 5: Angle 4 (B-E-F) and angle 5 (the right angle) are indeed adjacent angles because they share a vertex (E) and a side (EF) and are next to each other.

3. Angle 2 and angle 3: Angle 2 (A-E-D) and angle 3 (D-E-B) are formed on a straight line (line C-D). Since they form a linear pair, they are indeed supplementary angles, adding up to 180 degrees.

4. Angle 1 and angle 4: Angle 1 (A-E-C) and angle 4 (B-E-F) are not vertical angles; they are adjacent angles.

5. Angle 1 and angle 5: Angle 1 (A-E-C) and angle 5 (right angle) are not supplementary because they do not add up to 180 degrees.

Based on the analysis, the two true statements are:

C. Angle 2 and angle 3 are supplementary angles.

B. Angle 4 and angle 5 are adjacent angles.