Question

Construct a bisector of an angle of $ 60{}^\circ $

Answer 1

Hint: Angle of $ 60{}^\circ $ is greater than $ 90{}^\circ $ which means that $ 60{}^\circ $ angle is acute angle.
Half of the acute angle will also be an acute angle.

Complete step-by-step answer:

The figure above shows the angle, ∠DEF equal to $ 60{}^\circ $ .
Compass is used to draw an acute angle of $ 60{}^\circ $ . In triangles or many other types of polygons, a protractor is used to measure the angles and categorize them into different categories. On the basis of measure of angle, angles can be acute (less than $ 90{}^\circ $ ), obtuse (more than $ 90{}^\circ $ but less than $ 180{}^\circ $ ) and right angle (equal to $ 90{}^\circ $ ).
I.To draw an angle of measure of $ 60{}^\circ $ , first a line named ED is drawn which is the base of angle DEF equal to $ 60{}^\circ $ .

II.At end point E, the point of compass is put and an arc is drawn on line ED and from arc online ED, another arc is drawn. The arc from point E is extended to intersect another arc. The point of intersection of arcs and point E are connected and extended to point F.

III.Finally, point E is joined to point F leading in formation of angle, ∠DEF equal to $ 60{}^\circ $ .
Angle-bisectors divide an angle into two equal angles. The half of angle of measure $ 60{}^\circ $ is equal to angle of measure $ 30{}^\circ $ .

Note: As angle measuring $ 60{}^\circ $ is an acute angle, the ray of angle drawn using compass faces inward indicating angle of measure less than $ 90{}^\circ $ .