Question

How to construct a $105°$ angle?

Answer 1

Step 1 : Draw ray and a Semicircular arc.

• Draw a Ray $AB$ of any length fixed at end $A$
• Now, with $A$ as center and any radius draw a Semicircular arc intersecting $AB$ at $C$.

Step 2 : Draw two arcs Intersecting the Semicircular arc.

• With the same radius used to draw the Semicircular arc draw an arc with $C$ as center and intersecting the Semicircular arc at $D$. $D$ is at $60°$.
• Now with the same radius draw another arc centered at $D$ and intersecting the Semicircular arc at $G$. $G$is at $120°$.

Step 3: Draw the angle bisector of $G$ and $D$.

• Without changing the radius, first draw an arc centered at $D$ and then draw another arc centered at $G$ intersecting the arc centered at $D$ . Name the intersection point as $F$. $F$ is at $90°$.
• Join $F$ and $A$. Name the point as $E$ where line segment $AF$ intersects the semicircular arc.

Step 4 : Draw the angle bisector of $F$ and $G$ that will be $105°$.

• With the same radius, first draw an arc centered at $E$ and then draw another arc centered at $G$ intersecting the arc centered at $E$ . Name the intersection point as $H$. $H$ is at $105°$.

These are the steps to Construct a $105°$ angle.