The figure below shows two lines that intersect at point e along with ray ef

Question

. 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

To evaluate the statements based on the described configuration of angles and lines, let's analyze the relationships:

1. Angle 2 and angle 3: These angles are formed by the intersection of the two lines at point E. Angle 2 (A-E-D) and angle 3 (D-E-B) are on a straight line and thus supplementary.

   • True: Statement C (Angle 2 and angle 3 are supplementary angles).

2. Angle 1 and angle 5: Angle 1 (A-E-C) and angle 5 (right-angle F-E-C, which is 90 degrees) are angles that together form a straight angle at point E along line C-D. Since angle 1 is not specified as a right angle, these are not supplementary.

   • False: Therefore, Statement E is false.

3. Angle 4 (B-E-F) and angle 5 (right-angle F-E-C) are adjacent angles because they share a common vertex (E) and a common side (E-F to E-C).

   • True: Statement B (Angle 4 and angle 5 are adjacent angles).

4. Angle 2 and angle 5: Are not complementary because they do not add up to 90 degrees; instead, angle 5 is 90 degrees, and angle 2 is not defined as complementary to it.

   • False: Statement A is false.

5. Angle 1 and angle 4: Vertical angles are formed when two lines intersect. So Angle 1 (A-E-C) and angle 4 (B-E-F) are not vertical angles since they do not oppose each other at the intersection.

   • False: Statement D is false.

Given this analysis, the two statements that are true are:

C. Angle 2 and angle 3 are supplementary angles.

B. Angle 4 and angle 5 are adjacent angles.