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

To determine which statements are true based on the provided information about the angles formed by the intersecting lines and the perpendicular ray, we can analyze the relationships between the angles.

1. Angle 2 and angle 5 are complementary angles.

   • Angle 2 is one of the angles formed by line A-B and line C-D, while angle 5 is the right angle formed by ray E-F. Since angle 2 and angle 5 add up to 90 degrees (assuming angle 2 is not a right angle), they are indeed complementary angles.
   • This statement is true.

2. Angle 4 and angle 5 are adjacent angles.

   • Angle 4 is formed by ray E-F and line C-D, and angle 5 is a right angle also involving line C-D. These angles share the common side EF and are next to each other, making them adjacent angles.
   • This statement is true.

3. Angle 2 and angle 3 are supplementary angles.

   • Angle 2 and angle 3 are vertical angles formed by the intersection of the two lines. Vertical angles are equal, not supplementary. Therefore, angle 2 and angle 3 do not add up to 180 degrees.
   • This statement is false.

4. Angle 1 and angle 4 are vertical angles.

   • Angle 1 is adjacent to angle 2 and angle 4 is adjacent to angle 5, making them not vertical angles. Vertical angles are formed by two intersecting lines across from each other. Therefore, angle 1 and angle 4 are not vertical angles.
   • This statement is false.

5. Angle 1 and angle 5 are supplementary angles.

   • Angle 1 and angle 5 are not adjacent nor necessarily on a straight line together, but angle 1 and angle 5 do not sum up to 180 degrees since one is acute (angle 1) while angle 5 is a right angle.
   • This statement is false.

The correct answers to select from the statements are:

• A. Angle 2 and angle 5 are complementary angles.
• B. Angle 4 and angle 5 are adjacent angles.