The value of x, which represents the measure of ∠LMN, is 120°.
Here's a breakdown of the problem and solution:
Key Information:
- LMNO is a rectangle.
- m∠MON = 30°.
- We need to find the value of x.
Rectangle Properties:
- Rectangles have four right angles (90° angles).
- Opposite angles in a rectangle are equal.
Reasoning:
1. Angle MON: Since ∠MON is 30°, its opposite angle, ∠LOM, is also 30° (opposite angles in a rectangle).
2. Angle LMN: ∠LMN is adjacent to both ∠MON and ∠LOM, forming a straight line with them. Therefore, ∠LMN + ∠MON + ∠LOM = 180° (angles on a straight line).
3. Substitution: Substituting the known values, we get ∠LMN + 30° + 30° = 180°.
4. Solving for x: Simplifying the equation, we find ∠LMN = 180° - 60° = 120°.