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The image shows a diagram of intersecting lines with angles labeled as 34°, and the question asks for the value of \( y \).

### Solution:
The intersecting lines create pairs of vertical (opposite) angles, which are always equal. The 34° angles are opposite each other, so the corresponding vertical angles will also be 34°.

Given that the angle adjacent to \( y \) is 34° and the angle adjacent to it is \( y \), these two angles are supplementary because they are on a straight line. Supplementary angles sum up to 180°.

So, we have:
\[
y + 34° = 180°
\]
\[
y = 180° - 34°
\]
\[


Solve the geometry problem involving intersecting lines and find the value of y using the concepts of vertical and supplementary angles. This problem is suitable for students in Grades 6-8 and covers essential geometric principles.

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