Therefore the angles in a quadrilateral sum to 360°.Īll quadrilaterals sum to 360° because we can always draw two triangles inside them by connecting two opposite corners. The combination of both triangle angles makes the full angles of the quadrilateral. The 3 angles in each triangle add up to 180°. In the example below, we see the four-sided shape divided into two triangles.

Each triangle contains 180° and so, two triangles contain 360°.

Why do Angles in a Quadrilateral Sum to 360 Degrees?Īngles in a quadrilateral add to 360° because two triangles can be made inside any quadrilateral by drawing straight lines from one corner to the other corners. For a quadrilateral, n = 4 and so the (n-2) becomes 4 – 2 which equals 2.Ģ × 180° = 360° and so, all 4 angles in a quadrilateral add to 360°. In a quadrilateral, we can only form 2 triangles. Every time a new side is added, a new triangle can be formed. The (n-2) part of the formula tells us how many triangles can be drawn inside any polygon. The formula for the sum of the angles in any polygon is (n-2) × 180°. Therefore the sum of the angles in a quadrilateral is 360°. A quadrilateral has 4 sides and so, n = 4. The formula for the sum of the angles in a polygon is (n-2) × 180°, where n is the number of sides. We can check the angles in our parallelogram by making sure that all 4 angles add to 360°.ġ20° + 120° + 60° + 60° = 360° and so, the result is correct. Therefore 120° + b = 180° and angle b = 60°.ī and c are opposite to each other, so we can see that they too are equal. The angle opposite to this angle is the same size and so, angle a = 120°.Īngles b and c are both next to the 120° angle. In the example below, one angle is known to be 120°. To find missing angles in a parallelogram, use the following rules: If one angle in a parallelogram is known, all other angles can be calculated. The second step is to subtract this result from 360°.ģ60° – 300° = 60° and so, the missing angle is 60°. The first step is to add up the 3 known angles. To find a missing angle in a quadrilateral, add up the 3 known angles and subtract this result from 360°.įor example, here is a quadrilateral containing 3 known angles of 75°, 85° and 140°. The 4 angles in a quadrilateral always add up to 360°. How to Find a Missing Angle in a Quadrilateral Here are some more examples of quadrilaterals where the angles are shown adding up to 360°. Quadrilaterals also always have 4 angles.įor example, the 4 angles in a rectangle are all 90°. This rule is true for all quadrilaterals.Ī quadrilateral is any 4-sided shape. The four angles in a quadrilateral always add up to 360°. What do the Angles in a Quadrilateral Add Up to?

Quadrilateral angles