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Multiple Select Question

The figure below shows two lines that intersect at point
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.

1 answer

To determine which statements are true, let's analyze the relationships between the angles based on the given descriptions.

  1. Angle 2 and angle 5 are complementary angles: Complementary angles add up to 90 degrees. Angle 5 is a right angle (90 degrees). Angle 2 and angle 5 together will make 90 degrees. Therefore, this statement is true.

  2. Angle 4 and angle 5 are adjacent angles: Adjacent angles share a common side and a common vertex. Angle 4 (B-E-F) and angle 5 (right angle F-E-C) do share the vertex E and are next to each other, making them adjacent angles. Therefore, this statement is true.

  3. Angle 2 and angle 3 are supplementary angles: Supplementary angles add up to 180 degrees. Angle 2 (A-E-D) and angle 3 (D-E-B) are formed along the same line, implying they are supplementary. Therefore, this statement is true.

  4. Angle 1 and angle 4 are vertical angles: Vertical angles are opposite angles formed by two intersecting lines. Angle 1 (A-E-C) and angle 4 (B-E-F) are not opposite angles, so this statement is false.

  5. Angle 1 and angle 5 are supplementary angles: Angle 1 and angle 5 do not share a common side and do not add up to 180 degrees. Thus, this statement is false.

Based on this analysis, the two statements that apply are:

  • A. Angle 2 and angle 5 are complementary angles.
  • C. Angle 2 and angle 3 are supplementary angles.

Thus, the correct answers are A and C.