Angles in squares and rectangles
Square
A square has four right angles (90°).
Each diagonal splits a corner into two angles of 45°.
Note also that the diagonals cut each other in half at right angles.
Rectangle
A rectangle has four right angles.
The diagonals are equal and split a rectangle into four isosceles triangles.
The diagonals do not meet at right angles.
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:
\(x^\circ = 180^\circ - (20^\circ + 20^\circ ) = 180^\circ - 40^\circ = 140^\circ\)
