Use the image to answer the question.

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 ?

(1 point)

Answer 1

To find the angle that is complementary and adjacent to ∠5, we need to identify its position relative to the other angles.

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

Since ∠5 is located in the third quadrant and is formed by the intersection of the increasing line and one of the perpendicular lines, we can determine its adjacent angles based on their positions:

• In the third quadrant, the angles are labeled as follows:
  • ∠5 is adjacent to ∠4 (to the left) and ∠6 (to the right).

Now, we need to assess which of these adjacent angles is complementary to ∠5:

• ∠4 is located in the second quadrant and would be larger than 90 degrees (since it is one of the right angles in the second quadrant).
• ∠6, on the other hand, is adjacent in the third quadrant and would be smaller than 90 degrees.

Since the total angle around a point is 360 degrees, in the third quadrant, if ∠5 is one of the angles formed by the increasing line and continues to ∠6, then for the angles two adjacent angles (∠5 and ∠6) to sum up to 90 degrees, it must mean that ∠6 is actually complementary to ∠5.

Therefore, the angle that is complementary and adjacent to ∠5 is:

Angle 6.