A carpenter makes wooden chairs. He has enough wood to make 30 chairs.
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair.
He only has 40 hours available to work on chairs.

The carpenter wants to maximize his profit given the information above.

How many dining chairs and rocking chairs should he make?
How much profit does he earn?

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.