The amphitheater has two types of tickets available, reserved seats and lawn seats. the maximum capacity of the venue is 20,000 people, however, they must sell at least 5,000 tickets for a concert to be held. as an additional constraints, the number of lawn seats cannot exeed the number of reserved seats. if reserved seats profit $65 each and lawn tickets profit $40 each, how many of each must they sell to maximize their profits?

the answer is 99.

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.