identifying linear pair
the figure below, give the following.
(a) one pair of angles that form a linear pair
(b) one pair of vertical angles
(c) one pair of angles that are congruent
figure with lines l, m, n and angles numbered 1, 2, 5, 6 (around line l) and 3, 4, 7, 8 (around line m intersecting line n)
(a) linear pair: ∠□ and ∠□
(b) vertical angles: ∠□ and ∠□
(c) congruent angles: ∠□ and ∠□

Question

Accepted Answer

### Part (a): Linear Pair
# Explanation:
## Step1: Recall linear pair definition
A linear pair of angles are adjacent and supplementary (sum to $180^\circ$), forming a straight line.
## Step2: Identify adjacent angles on a line
Angles $\angle 5$ and $\angle 1$ are adjacent and form a straight line (along line $l$ and transversal $n$). Another example: $\angle 6$ and $\angle 2$, or $\angle 7$ and $\angle 3$, $\angle 8$ and $\angle 4$, $\angle 5$ and $\angle 6$, etc. Let's take $\angle 5$ and $\angle 6$ (they are adjacent and form a straight line along $n$ with line $l$).
# Answer (a): $\angle 5$ and $\angle 6$ (other valid pairs: $\angle 1$ & $\angle 2$, $\angle 7$ & $\angle 8$, $\angle 3$ & $\angle 4$, $\angle 5$ & $\angle 1$, etc.)

### Part (b): Vertical Angles
# Explanation:
## Step1: Recall vertical angles definition
Vertical angles are opposite angles formed by two intersecting lines, and they are congruent.
## Step2: Identify intersecting lines
Lines $l$ and $n$ intersect, forming $\angle 5$ & $\angle 2$, $\angle 6$ & $\angle 1$. Lines $m$ and $n$ intersect, forming $\angle 7$ & $\angle 4$, $\angle 8$ & $\angle 3$. Let's take $\angle 5$ and $\angle 2$ (opposite angles from intersecting $l$ and $n$).
# Answer (b): $\angle 5$ and $\angle 2$ (other valid pairs: $\angle 6$ & $\angle 1$, $\angle 7$ & $\angle 4$, $\angle 8$ & $\angle 3$)

### Part (c): Congruent Angles
# Explanation:
## Step1: Recall congruent angles (equal measure)
Vertical angles are congruent (from part b). Also, if lines are parallel (implied if $l \parallel m$ as they are both perpendicular or same slope), corresponding angles are congruent. Here, $\angle 5$ and $\angle 7$ (if $l \parallel m$, corresponding angles) or vertical angles (like $\angle 5$ & $\angle 2$ from part b). Let's use vertical angles: $\angle 5$ and $\angle 2$ (congruent as vertical angles).
## Step2: Confirm congruence
Vertical angles are always congruent, so $\angle 5 \cong \angle 2$.
# Answer (c): $\angle 5$ and $\angle 2$ (other valid: $\angle 6$ & $\angle 1$, $\angle 7$ & $\angle 4$, $\angle 8$ & $\angle 3$, or corresponding angles if $l \parallel m$ like $\angle 5$ & $\angle 7$, $\angle 1$ & $\angle 3$, etc.)

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QUESTION IMAGE

Question

Explanation:

Part (a): Linear Pair

Step1: Recall linear pair definition

Step2: Identify adjacent angles on a line

Step1: Recall vertical angles definition

Step2: Identify intersecting lines

Step1: Recall congruent angles (equal measure)

Step2: Confirm congruence

Answer:

Part (b): Vertical Angles