Question

In the process of construction of ${45}^{\circ }$, what is the sum of all the other angles you would be constructing during the course?

Answer 1

Following are steps of construction:

Draw a line. With any point, say O as centre and any radius, draw an arc which cuts this line in A and B. We now have an angle of ${180}^{\circ }$(∠AOB). With A and B as centres and any radius more than $\frac{1}{2}$(AB), draw arcs which cut each other in C. Join OC, now ∠COB = ${90}^{\circ }$. If we bisect this angle, we will get ${45}^{\circ }$.

So, the sum of the intermediate angles = ${180}^{\circ }$ + ${90}^{\circ }$ = ${270}^{\circ }$