Question

If LMNO is a rectangle and m∠MON = 30°, what is the value of x? Option 1: x = 45° Option 2: x = 60° Option 3: x = 90° Option 4: x = 120°

Answer 1

Option 2: x = 60° In a rectangle, opposite angles are congruent. As angle MON is 30°, its opposite angle is also 30°. With four right angles totaling 360°, subtracting known angles (90° + 90°) leaves 180°. Deducting the two 30° angles from this sum gives x = 60°.

Step-by-step explanation:

In a rectangle, opposite angles are equal. Therefore, angle MON is also 30°. In a rectangle, the sum of all angles is 360°. Given that two angles are 90° each (as a rectangle has four right angles), subtracting these angles' measures from the total gives us 360° - 90° - 90° = 180°. As two angles are 30° each, their combined measure is 60° (180° - 30° - 30° = 60°), making x = 60°.

To further explain, a rectangle has four right angles, each measuring 90°. The total angle measure in any quadrilateral is 360°. Subtracting the known angles from this total leaves the remaining angles to sum up to 180°. With two angles known as 30° each, their combined measure is 60°, satisfying the value for angle x in the rectangle as x = 60°.

Answer 2

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°.