https://file.aiquickdraw.com/mathbot/file/1728494431181mo8nzhyw.jpg

To find the measure of angle \( x \), we can use the properties of intersecting lines and adjacent angles. From the image:

1. The angles \( 137^\circ \) and \( x \) are supplementary, meaning their measures must add up to \( 180^\circ \) because they form a linear pair.
   
Thus, we can set up the equation:

\[
137^\circ + x = 180^\circ
\]

Solving for \( x \):

\[
x = 180^\circ - 137^\circ = 43^\circ
\]

Therefore, the measure of \( x \) is:

\[
\boxed{43^\circ}
\]

Would you like further details or have any questions?

Here are some related questions:
1. What are adjacent angles, and how do they relate to supplementary angles?
2. How do you identify vertical angles in a set of intersecting lines?
3. Can you explain why angles on a straight line always add up to 180 degrees?
4. How can this knowledge of linear pairs help solve more complex geometric problems?
5. How would the approach change if the given angles were inside a polygon?

**Tip:** When dealing with intersecting lines, always remember that vertical angles are congruent, and adjacent angles on a straight line are supplementary.

Find the measure of angle x, given that two intersecting lines form angles of 137° and 35°.

Learn how to find the measure of angle x using the concept of supplementary angles. Two intersecting lines create angles of 137° and 35°, and you'll use the fact that angles forming a linear pair sum to 180°. Suitable for students in Grades 6-8.

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