A2. Three identical isosceles triangles fit exactly (without overlap) into a square, with two of the triangles having edges in common with the square, as shown in the diagram. What is the size of the shaded angle?
Solution
$15^{\circ}$

As the three isosceles triangles are identical, the three angles which meet in the bottom left-hand corner of the square are all equal. So each one is $90^{\circ} \div 3=30^{\circ}$. In each triangle, the other two angles are equal. Hence each is $(180-30)^{\circ} \div 2=75^{\circ}$.
Therefore the shaded angle is $(90-75)^{\circ}=15^{\circ}$.