The figure below shows two lines that intersect at point E

Question

along with ray EF

. 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 analyze the relationships between the angles, let's summarize the relationships given in the figure and definitions:

1. Angles 1 and 2 are adjacent angles (they share a common side and vertex).
2. Angle 2 and angle 3 are adjacent angles that also form a linear pair, thus they are supplementary (sum to 180 degrees).
3. Angle 4 is adjacent to angle 5, with angle 5 being a right angle (90 degrees).
4. Angles 1 and 3 are also adjacent but correspond to the perpendicular ray EF with angle 5.
5. Angles 1 and 4 cannot be vertical angles as they are not formed by two intersecting lines but rather from a ray intersecting the lines at E.

Now, let’s analyze the options:

A. Angle 2 and angle 5 are complementary angles.

• False. Angle 2 is not complementary (not adding up to 90 degrees) to angle 5.

B. Angle 4 and angle 5 are adjacent angles.

• True. They share a common vertex and a side.

C. Angle 2 and angle 3 are supplementary angles.

• True. They form a linear pair and add to 180 degrees.

D. Angle 1 and angle 4 are vertical angles.

• False. Vertical angles are formed by two intersecting lines, which does not apply here.

E. Angle 1 and angle 5 are supplementary angles.

• False. Angle 5 is a right angle while angle 1 is not necessarily 90 degrees.

Thus, the two true statements are:

B and C.