Question

Construct each of the following angles, using ruler and compasses:
${105}^o$

Answer 1

Step of construction

Construct a line segment $PQ$

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

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

Considering $S$ as centre and same radius, construct and arc which intersects the 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 point $U$

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

Considering $T$ and $V$ as centres and radius more than half of $TV$, construct arc intersecting in each other the point $W$

Join $PW$ which is makes ${105}^o$ with the ray $PQ$

Therefore, we know that $\angle WPQ={105}^o$.