Enter angle information
Interactive transversal diagram
Two parallel lines are crossed by one transversal. Select a relationship and angle pair. The highlighted angles update instantly for easier comparison.
Angles 3 and 5 are alternate interior angles.
Practice question generator
Generate a random geometry question. Choose one answer from four options. Immediate feedback explains the correct relationship clearly.
Calculation history
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|---|---|---|
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Formula used
How to use this calculator
Select the required calculation mode first. Choose the correct angle relationship next. Then enter values and press the calculate button.
Use algebra mode for expressions containing x. Parentheses and ordinary arithmetic operators are supported. Review warnings before accepting any geometric conclusion.
Open the diagram to compare named angle pairs. Adjust the transversal for another visual layout. Export finished results using the provided action buttons.
Example data
| First angle | Second angle | Relationship | Conclusion |
|---|---|---|---|
| 65° | 65° | Alternate interior | Angles are congruent |
| 112° | 112° | Corresponding | Angles are congruent |
| 75° | 105° | Same-side interior | Angles are supplementary |
| 48° | 52° | Alternate interior | Relationship is not satisfied |
Understanding alternate interior angles
Alternate interior angles lie between two crossed lines. They appear on opposite transversal sides. Parallel lines make each selected pair equal.
The converse theorem works in reverse. Equal alternate interior angles can prove parallel lines. The diagram must still match the theorem conditions.
Corresponding angles occupy matching intersection positions. Same-side interior angles total a straight angle. Vertical angles face across one shared intersection.
Frequently asked questions
What are alternate interior angles?
They sit between two lines. They occupy opposite transversal sides. Parallel lines make their measures exactly equal.
Must the lines be parallel?
Equality requires parallel lines in this theorem. Nonparallel lines may create different measures. Always confirm the diagram markings before concluding.
Can equal angles prove parallel lines?
Yes, the converse theorem allows that conclusion. The angles must be alternate interior angles. Correct placement remains essential for a valid proof.
What is a transversal?
A transversal crosses two or more lines. It creates several recognizable angle relationships. Those relationships support many standard geometry proofs.
How are same-side interior angles different?
They occupy the same transversal side. Parallel lines make them supplementary. Their combined measure therefore equals 180 degrees.
Does the calculator support radians?
Yes, choose radians from the unit selector. Numeric inputs are then interpreted as radians. Results remain available with selected decimal precision.
Which algebraic expressions are supported?
The parser supports linear expressions only. It accepts x, parentheses, and arithmetic operators. Nonlinear products are rejected for safer calculations.
Why was my angle rejected?
Geometry angles must remain within useful limits. Zero and straight angles are excluded. Check units, signs, and expression results carefully.
Can I save the result?
Yes, use CSV or PDF controls. The copy button stores plain result text. Browser history also keeps recent successful calculations.