Question

construct the angle pqr is 60 .now construct its complement at the point q.

Answer 1

draw a line segment QP
AT the point Q draw an arc that QP at C
At the point C, draw another arc which cuts the previous arc at D
Join Q to D. It is 60 degrees

Complement angles have the sum of 90 degree
Complement of 60 is 60+ 30= 90
Bisect angle PQD to get the angle of 30 degree
Take C and D as initial point and radius equal to more than half of CD. 
draw arcs intersecting each other at E
Join Q to E
This is complimentry angle 

Answer 2

Draw a line segment QP 

 

With initial point at Q with some convenient radius draw an arc cutting QP at C 

 

With C as center and radius = QC, draw an arc cutting the previous arc at point D 

 

Join QD 

 

Angle PQD = 60° 

 

Complementary angles means the sum is 90 ° 

 

So the complement of 60 degree is 30 degree 

 

Now construct angle of 30° which will be known as bisector of PQD 

 

Now take C and D as initial points and radius = more than half of CD 

 

Now draw arcs intersecting each other at E 

 

Join QE. Angle PQE = complement of 60 degree which is equal to 30 degrees.