11. $overleftrightarrow{gi}$ and $overleftrightarrow{jl}$ are parallel lines. which angles are adjacent angles? options: $angle lkm$ and $angle jhk$, $angle jhk$ and $angle lkh$, $angle ghf$ and $angle ihf$, $angle jkh$ and $angle lkm$. 12. $overleftrightarrow{oq}$ and $overleftrightarrow{rt}$ are parallel lines. which angles are corresponding angles? options: $angle qpm$ and $angle tsu$, $angle tsp$ and $angle tsu$, $angle rsu$ and $angle rsp$, $angle qps$ and $angle tsu$. 13. $overleftrightarrow{rt}$ and $overleftrightarrow{uw}$ are parallel lines. which angles are supplementary angles? options: $angle tsq$ and $angle uvx$, $angle rsq$ and $angle tsv$, $angle rsv$ and $angle wvs$, $angle uvs$ and $angle wvs$. 20. look at this diagram: (diagram with $overleftrightarrow{lm}$ and $overleftrightarrow{oq}$ parallel, $angle qpm = 50^circ$). if $overleftrightarrow{lm}$ and $overleftrightarrow{oq}$ are parallel lines and $mangle qpm = 50^circ$, what is $mangle lpm$?

Question

Accepted Answer

### Problem 11 (Adjacent Angles)
# Explanation:
## Step1: Recall Adjacent Angles Definition
Adjacent angles share a common side and vertex, and no overlapping.
## Step2: Analyze Each Option
- $ \angle LKM $ and $ \angle JHK $: No common side/vertex.
- $ \angle JHK $ and $ \angle LKH $: Share side $ HK $, vertex $ H $, adjacent.
- $ \angle GHF $ and $ \angle IHF $: Share side $ HF $, vertex $ H $, but are supplementary (linear pair), also adjacent. Wait, but let's check the diagram (parallel lines $ \overleftrightarrow{GJ} $ and $ \overleftrightarrow{IL} $, transversal $ \overleftrightarrow{MF} $).
Wait, maybe the intended answer is $ \angle JHK $ and $ \angle LKH $ (or $ \angle GHF $ and $ \angle IHF $, but let's recheck). Wait, adjacent angles are next to each other. $ \angle JHK $ and $ \angle LKH $: $ H $ is vertex? Wait, maybe typo. Wait, the options: $ \angle LKM $ (vertex $ K $), $ \angle JHK $ (vertex $ H $) – no. $ \angle JHK $ and $ \angle LKH $: If $ K $ and $ H $ are connected? Wait, maybe the correct adjacent angles are $ \angle JHK $ and $ \angle LKH $ (share a side at $ K $ or $ H $? Maybe the diagram shows $ \overleftrightarrow{JL} $ and $ \overleftrightarrow{GI} $ parallel, transversal $ \overleftrightarrow{MN} $. So $ \angle JHK $ and $ \angle LKH $ are adjacent (share side $ HK $, vertex $ K $? Wait, maybe the answer is $ \angle JHK $ and $ \angle LKH $.

# Answer: $ \angle JHK $ and $ \angle LKH $

### Problem 12 (Parallel Lines)
# Explanation:
## Step1: Recall Parallel Lines Definition
Lines that never intersect, same slope (in coordinate terms) or equal corresponding angles.
## Step2: Analyze the Diagram
The lines $ \overleftrightarrow{OQ} $ and $ \overleftrightarrow{RT} $ (from the diagram: $ O, P, Q $ on one line; $ R, S, T $ on another, cut by transversal $ \overleftrightarrow{NU} $). These lines are parallel (no intersection, same direction).

# Answer: $ \overleftrightarrow{OQ} $ and $ \overleftrightarrow{RT} $

### Problem 13 (Supplementary Angles)
# Explanation:
## Step1: Recall Supplementary Angles
Sum to $ 180^\circ $.
## Step2: Analyze Each Option
- $ \angle TSQ $ and $ \angle UVX $: Maybe equal (corresponding), not supplementary.
- $ \angle RSQ $ and $ \angle TSV $: Vertical angles, equal.
- $ \angle RSV $ and $ \angle WVS $: If $ \overleftrightarrow{UW} \parallel \overleftrightarrow{TR} $, $ \angle RSV + \angle WVS = 180^\circ $ (same - side interior angles).
- $ \angle UVS $ and $ \angle WVS $: Adjacent, sum to $ 180^\circ $ (linear pair), supplementary. Wait, but let's check the diagram: $ \overleftrightarrow{UW} \parallel \overleftrightarrow{TR} $, transversal $ \overleftrightarrow{XQ} $. $ \angle RSV $ (at $ S $) and $ \angle WVS $ (at $ V $): same - side interior, supplementary. Or $ \angle UVS $ and $ \angle WVS $ (linear pair). But the option $ \angle RSV $ and $ \angle WVS $ is supplementary.

# Answer: $ \angle RSV $ and $ \angle WVS $

### Problem 20 (Angle Calculation)
# Explanation:
## Step1: Identify Parallel Lines and Angles
$ \overleftrightarrow{LM} \parallel \overleftrightarrow{OQ} $ (given), transversal $ \overleftrightarrow{RK} $. $ \angle ZQPM = 50^\circ $ (let's assume $ \angle QPM = 50^\circ $, corresponding angle to $ \angle LMP $? Wait, $ \angle QPM $ and $ \angle LMP $ are corresponding angles (parallel lines, transversal), so $ \angle LMP = 50^\circ $. Wait, the question is "If $ \overleftrightarrow{LM} $ and $ \overleftrightarrow{OQ} $ are parallel lines and $ m\angle QPM = 50^\circ $, what is $ m\angle LMP $?"
## Step2: Corresponding Angles Postulate
Corresponding angles are equal when lines are parallel. So $ m\angle LMP = m\angle QPM = 50^\circ $.

# Answer: $ 50^\circ $

### Corresponding Angles (Problem with $ \overleftrightarrow{OQ}, \overleftrightarrow{RT} $)
# Explanation:
## Step1: Recall Corresponding Angles
Angles in same position relative to parallel lines and transversal.
## Step2: Analyze Options
- $ \angle QPM $ and $ \angle TSU $: Corresponding (same position, parallel lines $ \overleftrightarrow{OQ} \parallel \overleftrightarrow{RT} $, transversal $ \overleftrightarrow{NU} $).
- $ \angle TSP $ and $ \angle TSU $: Adjacent, not corresponding.
- $ \angle RSU $ and $ \angle RSP $: Adjacent, not corresponding.
- $ \angle QPS $ and $ \angle TSU $: Not same position.

# Answer: $ \angle QPM $ and $ \angle TSU $

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QUESTION IMAGE

Question

Explanation:

Problem 11 (Adjacent Angles)

Step1: Recall Adjacent Angles Definition

Step2: Analyze Each Option

Step1: Recall Parallel Lines Definition

Step2: Analyze the Diagram

Step1: Recall Supplementary Angles

Step2: Analyze Each Option

Answer:

Problem 12 (Parallel Lines)