https://file.aiquickdraw.com/mathbot/file/1729536820695na79q89h.jpg

In this image, two lines \( \ell_1 \) and \( \ell_2 \) are crossed by a transversal \( t \), and you need to find the value of \( x \) that makes \( \ell_1 \parallel \ell_2 \). The angles involved are labeled as \( x \) and \( 21^\circ \).

### Step-by-Step Solution:

To make \( \ell_1 \parallel \ell_2 \), the two angles must be either **corresponding angles** or **alternate interior angles**, depending on their positions. From the image, it appears these are **alternate interior angles**, which means they must be equal for the lines to be parallel.

Therefore:
\[
x = 21^\circ
\]

Thus, the value of \( x \) that makes \( \ell_1 \parallel \ell_2 \) is:
\[
x = 21^\circ
\]

Would you like any additional clarifications or details?

Here are some related questions:
1. What are alternate exterior angles, and how do they relate to parallel lines?
2. What would happen if the angles were supplementary instead of equal?
3. Can you find the value of \( x \) if the transversal created consecutive interior angles?
4. How do corresponding angles differ from alternate interior angles?
5. How would the solution change if the angles were given in terms of algebraic expressions?

**Tip:** Remember that for lines to be parallel, alternate interior angles must be equal, and corresponding angles must also be equal.

Find the value of x that makes l1 parallel to l2, with angles x and 21 degrees.

Learn how to find the value of x that makes two lines parallel, using the alternate interior angle theorem. This example involves a 21-degree angle and covers key geometric concepts about transversals and parallel lines. Suitable for students in Grades 7-9.

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