Geometry Angle Calculator and Simulator: Triangles, Parallel Lines, Circles and Polygons
Free interactive geometry lab: drag triangle corners to see angles, sides, area and similar triangles; explore parallel lines and transversals (corresponding, alternate, co-interior angles); test circle theorems; classify any angle and find polygon angle sums.
Drag the corners A, B and C (or focus one and use the arrow keys). Everything updates as you move.
Click any numbered angle to see how every other angle is related to it. Drag the top of the transversal to turn it.
Drag the lettered points around the circle.
Angle explorer
Polygon angles
Learn angles and geometry by moving things
This lab lets you drag points and lines and watch the angles recalculate. In the Triangles tab, move the corners to see the angle sum stay at 180°, how the triangle is named (acute, right or obtuse; scalene, isosceles or equilateral), its area, circumcircle, incircle, centroid and orthocentre, and add a similar triangle to see why corresponding angles stay equal while sides and areas scale. In Parallel lines you get the eight angles made by a transversal and the names corresponding, alternate interior, alternate exterior, co-interior and vertical. In Circles you can test the central-angle theorem, Thales' theorem, cyclic quadrilaterals and the tangent-chord theorem. Angles & polygons classifies any angle and shows interior and exterior angle sums.
Key facts
| Fact | Rule |
|---|---|
| Triangle angle sum | A + B + C = 180° |
| Exterior angle of a triangle | equals the sum of the two opposite interior angles |
| Similar triangles (AA) | two equal angles → all angles equal, sides in the same ratio k, areas in ratio k² |
| Parallel lines + transversal | corresponding and alternate angles are equal; co-interior angles add to 180° |
| Vertical angles | always equal |
| Linear pair | adjacent angles on a straight line add to 180° |
| Inscribed angle theorem | the angle at the centre is twice the angle at the circumference on the same arc |
| Thales' theorem | an angle in a semicircle is 90° |
| Cyclic quadrilateral | opposite angles add to 180° |
| Polygon with n sides | interior angles add to (n − 2) × 180°; exterior angles add to 360° |
Questions
- How do I know if two triangles are similar?
- If two angles of one equal two angles of the other (AA), or all three side ratios match (SSS), or two side ratios and the angle between them match (SAS).
- What is a transversal?
- A line that crosses two other lines. It makes eight angles; when the two lines are parallel the angles fall into just two sizes, θ and 180° − θ.
- Is my data private?
- Nothing is sent anywhere: it all runs in your browser.
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