Quadrilaterals

Angles in a quadrilateral add up to 360°.

Square

A square has four equal sides and four right angles.

Diagram of a square

Each diagonal splits a corner into two angles of 45^\circ.

Two isosceles triangles joined at the base to form a square with the 45° base angles

Note also that the diagonals are equal and cut each other in half at right angles. The diagonals are lines of symmetry giving the square 4 lines of symmetry in total.

Rectangle

A rectangle has opposite sides which are equal and parallel. It also has four right angles.

Diagram of a rectangle

The diagonals are equal and split a rectangle into four isosceles triangles. The diagonals are not lines of symmetry.

Diagram of a rectangle made up of 4 isosceles triangles

Question

Calculate the size of angle x^\circ.

Rectangle made of 4 isosceles triangles, one with a 70° angle, another with an x° angle

Since each corner of a rectangle is 90°, then the smaller top left corner angle is 90° - 70° = 20°.

Using the rectangle's lines of symmetry, we can see the other angles which are equivalent and then fill in any missing angles in each triangle.

4 isosceles triangles forming a rectangle. 70° and 40° angles and 20° and 140° angles

Using the isosceles triangle at the top:

x^\circ  = 180^\circ  - (20^\circ  + 20^\circ ) = 180^\circ  - 40^\circ  = 140^\circ