Question

Construct incircle of $△SGN$ such that SG=6.7 cm, $\angle S={70}^o$, $\angle G={50}^o$.

Answer 1

1. Draw a line $SG$ of length $6.7cm$

2. We have to construct ${70}^o$ at $S$. Take any angle length on compass, draw an arc $X{X}^{\prime }$. Place the compass of $X$ and cut two arcs $(1$ and $2$). From there two arcs, cut another arc at $3$. With the same measure compass needle at $3,$ cut arc $4$ and extend it down.

3. By measuring the length $2x$ by a compass (the dotted lines). Place the compass at $1$ and cut the arc at $4$. Both arc will meet at a point $z$ and mark ${70}^o$ at $S$

4. Now construct ${50}^o$ at $G$. Take out any length on a compass, cut the arc $Y{Y}^{\prime }$. With the same measure cut $y_1$ and $y_2$. Measure $y_1$ from $G$ and cut an arc. Similarly measure $y_2$ from $G$ and cut an arc. They meet at $C$. Join the lines $Z$ and $CC$. Now we get point $N$.

$\therefore$ We get $△SNG$