Question

Use the image to answer the question.

An illustration shows 6 angles formed by 3 intersecting lines. Two perpendicular lines form 4 right angles with each other, and the third increasing line passes through origin and the first and third quadrants. Starting from the second quadrant, the angles are labeled in a clockwise direction as 1, 2, 3, 4, 5, and 6. In the first quadrant, the increasing line divides the perpendicular angle in two parts, angle 2 and angle 3. In the third quadrant, the increasing line divides the perpendicular angle in two parts angle 5 and 6.

Angles are numbered 1–6. Which angle number is complementary and adjacent to ∠5
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(1 point)

1 answer

To determine which angle is complementary and adjacent to ∠5, we need to understand the relationships between the angles formed by the three intersecting lines.

  1. Complementary Angles: Two angles are complementary if the sum of their measures is 90 degrees.
  2. Adjacent Angles: Two angles are adjacent if they share a common side and a common vertex.

From your description, angles are labeled in the following way:

  • In the first quadrant: angles 2 and 3 (formed by the increasing line and the two vertical/horizontal lines)
  • In the second quadrant: angle 1 (the top left angle)
  • In the third quadrant: angles 5 and 6 (formed by the increasing line and the two vertical/horizontal lines)
  • In the fourth quadrant: angle 4 (the bottom right angle)

Since angle 5 is in the third quadrant, the adjacent angle to it in that quadrant is angle 6.

Furthermore, the relationship between angle 5 and angle 6 can be analyzed:

  • Angles 5 and 6, together with their respective adjacent angles (which in this case would also include angle 4), would determine the total angles.

While we aren't given specific values, if we assume the intersecting perpendicular lines create right angles (90 degrees), then angles 5 and 6 are positioned such that they can either sum to 90 degrees or not, depending on what angle 6 is measured.

In the case described:

  • Angle 6 is not complementary to angle 5 because it does not sum to 90 degrees.
  • Instead, the angle adjacent to angle 5 that would complement it more directly is angle 4. Specifically, angle 5 and angle 4 would be complementary if their sum equals 90 degrees.

Conclusion: The angle that is complementary and adjacent to ∠5 is ∠4.