using the figure below, state the transversal that forms each pair of angles. then identify the special name for the angle pair.
16) ∠1 and ∠12 transversal = ______ special name = ________
17) ∠2 and ∠10 transversal = ______ special name = ________
18) ∠4 and ∠9 transversal = ______ special name = ________
19) ∠6 and ∠3 transversal = ______ special name = ________
20) ∠14 and ∠10 transversal = ______ special name = ________

Question

using the figure below, state the transversal that forms each pair of angles. then identify the special name for the angle pair.
16) ∠1 and ∠12  transversal = ______  special name = ________
17) ∠2 and ∠10  transversal = ______  special name = ________
18) ∠4 and ∠9   transversal = ______  special name = ________
19) ∠6 and ∠3   transversal = ______  special name = ________
20) ∠14 and ∠10 transversal = ______  special name = ________

Accepted Answer

### 16) $\angle 1$ and $\angle 12$
# Explanation:
## Step1: Identify transversal
A transversal is a line that intersects two or more lines. $\angle 1$ is on line $r$ and $m$, $\angle 12$ is on line $r$ and $k$. So the transversal is line $r$ (since it intersects $m$ and $k$).
## Step2: Identify angle pair
$\angle 1$ and $\angle 12$ are on opposite sides of transversal $r$, and are outside the two lines $m$ and $k$? Wait, no, $\angle 1$ is above $m$, $\angle 12$ is below $k$? Wait, actually, $\angle 1$ and $\angle 12$: $\angle 1$ is adjacent to $\angle 2$, $\angle 12$ is adjacent to $\angle 10$. Wait, line $r$ intersects $m$ and $k$. $\angle 1$ is on $m$ (above) and $r$ (left), $\angle 12$ is on $k$ (below) and $r$ (right). Wait, maybe they are vertical angles? No, vertical angles are opposite each other. Wait, $\angle 1$ and $\angle 3$ are vertical, $\angle 12$ and $\angle 10$ are vertical. Wait, maybe I made a mistake. Wait, the lines: $m$ and $k$ are parallel? $r$ and $t$ are transversals. Wait, $\angle 1$ is at the intersection of $r$ and $m$, $\angle 12$ is at the intersection of $r$ and $k$. So transversal is $r$. Now, the angle pair: $\angle 1$ is above $m$, left of $r$; $\angle 12$ is below $k$, right of $r$. Wait, maybe they are alternate exterior angles? Wait, no, $m$ and $k$ are the two lines (parallel), $r$ is transversal. $\angle 1$ is exterior to $m$ (left of $r$), $\angle 12$ is exterior to $k$ (right of $r$), and they are on opposite sides of $r$. Wait, maybe not. Wait, maybe they are same - side exterior? No, maybe I need to re - look. Wait, $\angle 1$ and $\angle 12$: $\angle 1$ is at $(r,m)$ top - left, $\angle 12$ is at $(r,k)$ bottom - right. Wait, actually, $\angle 1$ and $\angle 12$: the transversal is $r$, and the angle pair is "alternate exterior angles"? Wait, no, maybe "vertical angles" is wrong. Wait, let's list the lines:

Lines: $m$ (horizontal top), $k$ (horizontal bottom), $r$ (vertical left), $t$ (vertical right).

$\angle 1$: formed by $r$ and $m$, top - left.

$\angle 12$: formed by $r$ and $k$, bottom - right.

So transversal is $r$. The angle pair: since $m$ and $k$ are parallel (assumed, as they are horizontal), and $r$ is transversal, $\angle 1$ and $\angle 12$: $\angle 1$ is above $m$, $\angle 12$ is below $k$, on opposite sides of $r$. Wait, maybe "alternate exterior angles" is incorrect. Wait, maybe "corresponding angles"? No. Wait, maybe I made a mistake. Let's check the other angles.

Wait, maybe the correct transversal for $\angle 1$ and $\angle 12$ is $r$, and the special name is "alternate exterior angles"? Wait, no, $\angle 1$ is at $(r,m)$ top - left, $\angle 12$ is at $(r,k)$ bottom - right. The two lines cut by transversal $r$ are $m$ and $k$. So $\angle 1$ is exterior to $m$ (left of $r$), $\angle 12$ is exterior to $k$ (right of $r$), and they are on opposite sides of $r$. So alternate exterior angles.

# Answer:
transversal = $r$, special name = alternate exterior angles

### 17) $\angle 2$ and $\angle 10$
# Explanation:
## Step1: Identify transversal
$\angle 2$ is at $(r,m)$ top - right, $\angle 10$ is at $(r,k)$ top - right? Wait, no, $\angle 10$ is at $(r,k)$ top - left? Wait, the diagram: $r$ is vertical, $m$ is horizontal top, $k$ is horizontal bottom. So $\angle 2$ is above $m$, right of $r$; $\angle 10$ is above $k$, right of $r$. So the transversal is $r$, and the two lines cut by $r$ are $m$ and $k$.
## Step2: Identify angle pair
$\angle 2$ and $\angle 10$ are on the same side of transversal $r$ (right side) and above the two lines $m$ and $k$ (wait, $m$ is above $k$). So they are "corresponding angles" because they are in the same relative position with respect to the transversal and the two lines (both above the line, right of transversal).

# Answer:
transversal = $r$, special name = corresponding angles

### 18) $\angle 4$ and $\angle 9$
# Explanation:
## Step1: Identify transversal
$\angle 4$ is at $(r,m)$ bottom - right, $\angle 9$ is at $(r,k)$ bottom - left. The transversal is $r$, which intersects $m$ and $k$.
## Step2: Identify angle pair
$\angle 4$ is below $m$, right of $r$; $\angle 9$ is below $k$, left of $r$. They are on opposite sides of transversal $r$ and between the two lines $m$ and $k$ (since $m$ and $k$ are horizontal, the area between them). So they are "alternate interior angles".

# Answer:
transversal = $r$, special name = alternate interior angles

### 19) $\angle 6$ and $\angle 3$
# Explanation:
## Step1: Identify transversal
$\angle 6$ is at $(t,m)$ top - right, $\angle 3$ is at $(r,m)$ bottom - left. The line that intersects both $r$ and $t$ (the two transversals) and $m$ (the horizontal line) is $m$? Wait, no. Wait, $\angle 6$ is formed by $t$ and $m$, $\angle 3$ is formed by $r$ and $m$. So the transversal is $m$, which intersects $r$ and $t$.
## Step2: Identify angle pair
$\angle 6$ is above $m$, right of $t$; $\angle 3$ is below $m$, left of $r$. Wait, no, $\angle 3$ is at $(r,m)$ bottom - left, $\angle 6$ is at $(t,m)$ top - right. The two lines cut by transversal $m$ are $r$ and $t$. $\angle 3$ is below $m$, left of $r$; $\angle 6$ is above $m$, right of $t$. Wait, maybe they are "alternate exterior angles"? Wait, $r$ and $t$ are vertical lines (transversals), $m$ is horizontal. $\angle 3$ is exterior to the region between $r$ and $t$ (left of $r$), $\angle 6$ is exterior to the region between $r$ and $t$ (right of $t$), and on opposite sides of $m$ ( $\angle 3$ below, $\angle 6$ above). Wait, maybe "alternate exterior angles" is correct. Or maybe "corresponding angles"? No. Wait, let's re - think. The transversal is $m$, cutting $r$ and $t$. $\angle 3$ is at the bottom - left of $r - m$ intersection, $\angle 6$ is at the top - right of $t - m$ intersection. They are on opposite sides of $m$ and opposite sides of the region between $r$ and $t$. So alternate exterior angles.

# Answer:
transversal = $m$, special name = alternate exterior angles

### 20) $\angle 14$ and $\angle 10$
# Explanation:
## Step1: Identify transversal
$\angle 14$ is at $(t,k)$ top - right, $\angle 10$ is at $(r,k)$ top - right. The transversal is $k$, which intersects $r$ and $t$.
## Step2: Identify angle pair
$\angle 14$ is above $k$, right of $t$; $\angle 10$ is above $k$, right of $r$. They are on the same side of transversal $k$ (above $k$) and between the two lines $r$ and $t$ (the vertical lines). So they are "consecutive interior angles" (or same - side interior angles) because they are on the same side of the transversal and between the two lines. Wait, no, $\angle 10$ is at $(r,k)$ top - right, $\angle 14$ is at $(t,k)$ top - right. So they are on the same side of $k$ (above) and between $r$ and $t$ (the two vertical lines). So same - side interior angles (consecutive interior angles).

# Answer:
transversal = $k$, special name = same - side interior angles (consecutive interior angles)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

16) $\angle 1$ and $\angle 12$

Step1: Identify transversal

Step2: Identify angle pair

Step1: Identify transversal

Step2: Identify angle pair

Step1: Identify transversal

Step2: Identify angle pair

Answer:

17) $\angle 2$ and $\angle 10$