https://file.aiquickdraw.com/mathbot/file/17266513325621fg48h3y.jpg

Let's go through each question in the image:

### Problem 13:
We are given two parallel lines \( \ell \parallel m \), with one angle labeled \( 55^\circ \) and another labeled \( (x + 25)^\circ \). These angles appear to be corresponding angles, which means they are equal.

\[
55^\circ = x + 25^\circ
\]

Solve for \( x \):
\[
x = 55^\circ - 25^\circ = 30^\circ
\]

### Problem 14:
Here we have intersecting lines with a given angle of \( 95^\circ \) and another labeled \( (2x - 5)^\circ \). The two angles form a pair of vertically opposite angles, which means they are equal.

\[
95^\circ = 2x - 5^\circ
\]

Solve for \( x \):
\[
95^\circ + 5^\circ = 2x \implies 100^\circ = 2x \implies x = 50^\circ
\]

### Problem 15:
In this question, we have parallel lines \( \ell \parallel m \), with one angle labeled \( (6x - 33)^\circ \) and another labeled \( (2x + 26)^\circ \). These angles appear to be corresponding angles, which means they are equal.

\[
6x - 33^\circ = 2x + 26^\circ
\]

Solve for \( x \):
\[
6x - 2x = 26^\circ + 33^\circ \implies 4x = 59^\circ \implies x = \frac{59}{4} = 14.75^\circ
\]

### Problem 16:
In this case, we have parallel lines \( \ell \parallel m \), with one angle labeled \( 105^\circ \) and another labeled \( (3x - 18)^\circ \). These angles are consecutive interior angles, so their sum is \( 180^\circ \).

\[
105^\circ + (3x - 18)^\circ = 180^\circ
\]

Solve for \( x \):
\[
105^\circ - 18^\circ + 3x = 180^\circ \implies 87^\circ + 3x = 180^\circ \implies 3x = 93^\circ \implies x = 31^\circ
\]

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Would you like more details or further clarification on any of the steps? 

Here are 5 related questions to explore:
1. What are the properties of corresponding angles when two lines are parallel?
2. How do vertically opposite angles help in solving for unknowns?
3. What role do consecutive interior angles play in parallel line geometry?
4. How do we identify whether angles are supplementary or equal in these types of problems?
5. Can angles at intersections between non-parallel lines be solved similarly?

**Tip:** When working with parallel lines, always check for angle pairs like corresponding, alternate interior, or consecutive interior to set up equations efficiently.

Find the value of x for which the lines l and m are parallel.

In this problem, we explore how to solve for x by using the properties of parallel lines and angle relationships such as corresponding, vertically opposite, and consecutive interior angles. This problem is suitable for students in Grades 8-10.

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