Question 92
The figure consists of a square and a regular pentagon.
Calculate the sum of angles $a^\circ$ and $b^\circ$.
Useful facts (you may use them!): The interior angles of a triangle always sum to $180^\circ$. The interior angles of a quadrilateral always sum to $360^\circ$. To see this, divide the quadrilateral into two triangles by joining opposite vertices.
Each triangle has interior-angle sum $180^\circ$, giving $180^\circ\times2=360^\circ$ for the quadrilateral. The interior angles of a pentagon sum to $180^\circ\times3=540^\circ$, since any pentagon can be divided into three triangles as shown next.
Calculate the sum of angles $a^\circ$ and $b^\circ$.
Useful facts (you may use them!): The interior angles of a triangle always sum to $180^\circ$. The interior angles of a quadrilateral always sum to $360^\circ$. To see this, divide the quadrilateral into two triangles by joining opposite vertices.
Each triangle has interior-angle sum $180^\circ$, giving $180^\circ\times2=360^\circ$ for the quadrilateral. The interior angles of a pentagon sum to $180^\circ\times3=540^\circ$, since any pentagon can be divided into three triangles as shown next.