Question

Construct each of the following angles, using ruler and compasses:
${75}^o$

Answer 1

Step of construction

Construct a line segment

Considering $P$ as centre and any radius construct and arc which intersects the line $PQ$ at the point $R$

Considering $R$ as centre and same radius construct an arc which intersects the previous arc at the point $S$

Considering $S$ as centre and same radius construct an arc which intersect the previous arc in step $2$ at the point $T$

Considering $T$ and $S$ as centre and radius more than half of $TS$, construct arcs which intersects each other at the point $U$

Join the line $PU$ which intersects the arc in step $2$ at the point $V$

Considering $V$ and $S$ as centers and radius more than half of $VS$, construct arcs which intersects each others at the point $W$

Join the line $PW$

Therefore, we know that $\angle WPQ={75}^o$