Angle facts – angles at a point, parallel lines, triangle and polygon angle sums

What it shows

Angles on a straight line add up to 180°, angles around a point to 360°, and complementary angles to 90°; vertically opposite angles are equal. When a transversal crosses parallel lines, corresponding and alternate angles are equal and co-interior angles add up to 180°. These facts prove that the angles of a triangle add up to 180°: the line through one vertex parallel to the opposite side makes alternate angles. An n-sided polygon splits into n − 2 triangles, so its interior angles add up to (n − 2) × 180°, while its exterior angles always add up to 360°.

How to use

Choose a tab. In Angles at a point pick a Figure and drag the round handles. In Parallel lines choose an Angle pair, press Next pair and drag the transversal. In Triangle drag A, B or C, tick Exterior angle if you like, then press Tear off the angles. In Polygon set Number of sides n and tick Regular polygon. In Unknown angles type x and press Check.

Parameters you can change

• Mode Angles at a point, Parallel lines and a transversal, Angle sum and exterior angle of a triangle, Angles of a polygon, Unknown angles
• Figure (angles at a point) Angles on a straight line (two angles), Three angles on a straight line, Complementary angles, Intersecting lines (vertically opposite angles), Angles around a point
• Angle pair Corresponding, Alternate, Co-interior
• Angle between the transversal and the lines 20–160 °
• Show the exterior angle of the triangle
• Number of sides of the polygon n 3–12
• Regular polygon

Questions to explore

1. Why must the angles of every triangle add up to 180°, whatever its shape?
2. How many triangles does a diagonal split from one vertex make in a decagon?
3. Which regular polygons tessellate on their own, and why does a regular pentagon fail?