Angle Sum of a quadrilateral

Author:: Marc Azara

Topic:: Angles, Quadrilaterals

We already know the angles inside a triangle add up to 180^o. Any quadrilateral can be split into 2 triangles, as shown below. This means the angles must add up to 2 x 180 = 360^oMove the vertices of the quadrilateral to see that the angles always add up to 360^oWatch the brief video to see why.

Proving the angles in a quadrilateral add up to 360 degrees using 2 triangles

See if you can work out the missing angle B in the following quadrilaterals:

Write the answer without the degree symbol

The size of angle D is:

Check my answer

Did you figure out the method? Sample setting out:

= 84^o Use this method for the following questions.

Write the answer without the degree symbol

The size of angle D is:

Check my answer

Write the answer without the degree symbol

The size of angle D is:

Check my answer

Write the answer without the degree symbol

The size of angle D is:

Check my answer

Write the answer without the degree symbol

The size of angle D is:

Check my answer

Write the answer without the degree symbol

The size of angle D is:

Check my answer

We can also use other properties such as: - opposite angles in a parallelogram or rhombus are equal Click to see example - adjacent angles in a parallelogram add up to 180^o Click to see example y- This is also true for each pair of angles formed by the parallel lines in a trapezium . Click to see example - 1 pair of opposite angles are equal in a kite Click to see example Knowing the symmetry of shapes can be very helpful. Click the following links to see useful properties that we can see just from using lines of symmetry or rotational symmetry: Properties of a Kite Properties of a Rhombus