Question

practice

1. lines l, m, and n are parallel. find the value of x.

Explanation:

Step1: Identify Angle Relationships

Assuming the 45° angle and angle \( x \) are related via parallel lines (e.g., corresponding angles, alternate interior, or consecutive angles). If we consider the transversal creating a triangle or linear pair, but more likely, using the fact that when lines are parallel, corresponding angles or supplementary angles apply. Wait, maybe the 45° and \( x \) are supplementary? No, maybe vertical angles or alternate. Wait, perhaps the triangle has angles summing to 180, but if lines are parallel, maybe \( x = 180 - 45 - 90 \)? No, maybe the diagram shows a right angle? Wait, the user's diagram has a 45° and maybe a right angle (since there's a "2" and "3" maybe, but unclear. Wait, maybe it's a triangle with a 45° angle and a right angle, so the third angle is 45°, but no. Wait, perhaps the lines are parallel, so \( x \) and 45° are supplementary? No, maybe \( x = 135 \)? Wait, no, maybe the correct approach: if lines are parallel, and the transversal creates a linear pair with 45°, so \( x = 180 - 45 = 135 \)? Wait, no, maybe the angle is 45° and \( x \) is equal to 135°? Wait, maybe the diagram has a right angle, so 45 + 90 + x? No, maybe the correct answer is 135, but let's think again.

Wait, perhaps the lines are parallel, and the angle of 45° and \( x \) are same - side interior angles, so they are supplementary. So \( x + 45 = 180 \), so \( x = 180 - 45 = 135 \).

Step2: Solve for \( x \)

Using the supplementary angle relationship (since lines are parallel, same - side interior angles are supplementary):
\( x + 45^{\circ}=180^{\circ} \)
Subtract 45° from both sides:
\( x = 180^{\circ}- 45^{\circ}=135^{\circ} \)

Answer:

\( 135^{\circ} \)