1. What Are Vertical Angles?

Vertical angles are the angles opposite each other when two lines intersect. They are always equal to each other, regardless of the angle at which the lines intersect.

2. How Does the Calculator Work?

The calculator uses the vertical angle property:

Where:

• \( \theta \) — Given angle (degrees)
• \( \theta' \) — Vertical angle (degrees)

Explanation: When two lines intersect, they form two pairs of vertical angles. The angles in each pair are equal to each other.

3. Properties of Vertical Angles

Details: Vertical angles are always congruent, meaning they have equal measures. This property holds true regardless of the orientation of the intersecting lines.

4. Using the Calculator

Tips: Enter the known angle in degrees (0-360). The calculator will return the measure of its vertical angle, which will be identical to the input angle.

5. Frequently Asked Questions (FAQ)

Q1: Are vertical angles always equal?
A: Yes, vertical angles are always congruent (equal in measure) when two lines intersect.

Q2: Do vertical angles have to be acute?
A: No, vertical angles can be acute, right, or obtuse. They simply need to be opposite each other when two lines intersect.

Q3: Can vertical angles be supplementary?
A: Vertical angles themselves are equal, but adjacent angles formed by intersecting lines are supplementary (add up to 180°).

Q4: How are vertical angles different from adjacent angles?
A: Vertical angles are opposite each other and equal, while adjacent angles share a common side and vertex and are supplementary.

Q5: Do vertical angles apply to curved lines?
A: The concept of vertical angles specifically applies to straight lines that intersect. Curved lines have different geometric properties.