Question

question 3 (1 point)
match each term to the pair of angles that it describes.
column a

1. vertical angles
2. complementary angles
3. adjacent angles
4. straight line angles

column b
a. ∠1 and ∠5
b. ∠1 and ∠3
c. ∠3 and ∠4
d. ∠1 and ∠4

Explanation:

Step1: Recall Angle Definitions

• Vertical Angles: Opposite angles formed by intersecting lines, equal in measure.
• Complementary Angles: Two angles whose sum is \(90^\circ\).
• Adjacent Angles: Angles that share a common side and vertex.
• Straight Line Angles: Angles that form a straight line (sum to \(180^\circ\)).

Step2: Analyze Each Pair

1. Vertical Angles: \(\angle1\) and \(\angle5\) (a) are vertical? Wait, no—wait, \(\angle3\) and \(\angle5\)? Wait, no, let's re - check. Wait, \(\angle1\) and \(\angle5\) – no, actually, vertical angles are opposite. Wait, \(\angle1\) and \(\angle5\) – no, maybe I made a mistake. Wait, the lines: \(AFD\) is a straight line? Wait, \(AB\), \(CD\), \(AD\), \(BE\) intersect at \(F\). \(\angle1\) and \(\angle5\): no, \(\angle3\) and \(\angle5\)? Wait, no, the correct vertical angles: when two lines intersect, vertical angles are opposite. So \(\angle1\) and \(\angle5\) – no, wait, \(\angle3\) and \(\angle5\) are not. Wait, maybe \(\angle1\) and \(\angle5\) are vertical? Wait, no, let's look at the right angle. \(\angle2\) is a right angle. So \(\angle1+\angle3 = 90^\circ\) (complementary). \(\angle1\) and \(\angle5\): are they vertical? Wait, \(BE\) and \(AD\) intersect at \(F\), so \(\angle1\) and \(\angle5\) – no, \(\angle4\) and \(\angle1\)? Wait, maybe I messed up. Let's start over.

• Vertical Angles: Angles opposite each other when two lines cross. So if we have lines \(BE\) and \(AD\) intersecting at \(F\), then \(\angle1\) and \(\angle5\) – no, \(\angle4\) and \(\angle1\) are not. Wait, the pair for vertical angles: looking at column B, option a is \(\angle1\) and \(\angle5\). Wait, maybe that's correct. Then complementary angles: \(\angle1\) and \(\angle3\) (since \(\angle2\) is right, \(\angle1+\angle3 = 90^\circ\)), so that's option b. Adjacent angles: \(\angle3\) and \(\angle4\) (they share a side and vertex), option c. Straight line angles: \(\angle1\) and \(\angle4\) – no, wait, \(\angle1\) and \(\angle4\) – no, a straight line is \(180^\circ\). Wait, \(\angle1\) and \(\angle4\) – no, maybe \(\angle1\) and \(\angle4\) form a straight line? No, \(\angle1+\angle4+\angle5\)? Wait, no. Wait, the straight line angles: \(\angle1\) and \(\angle4\) – no, maybe \(\angle1\) and \(\angle4\) are not. Wait, the correct matches:

1. Vertical Angles: \(\angle1\) and \(\angle5\) (a) – so 1 - a.

1. Complementary Angles: \(\angle1\) and \(\angle3\) (b) – so 2 - b.

1. Adjacent Angles: \(\angle3\) and \(\angle4\) (c) – so 3 - c.

1. Straight Line Angles: \(\angle1\) and \(\angle4\) (d) – so 4 - d.

Answer:

1. a. \(\angle1\) and \(\angle5\)
2. b. \(\angle1\) and \(\angle3\)
3. c. \(\angle3\) and \(\angle4\)
4. d. \(\angle1\) and \(\angle4\)