Quadrilaterals
Angles in a A quadrilateral is a shape with four straight sides and four angles. add up to 360°.
Square
A square has four equal sides and four right angles.
Each diagonal splits a corner into two angles of \(45^\circ\).
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.
The diagonals are equal and split a rectangle into four isosceles triangles. The diagonals are not lines of symmetry.
Question
Calculate the size of angle \(x^\circ\).
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.
Using the isosceles triangle at the top:
\(x^\circ = 180^\circ - (20^\circ + 20^\circ ) = 180^\circ - 40^\circ = 140^\circ\)
