How many subsets of the set of divisors of 72 contain only composite numbers? for example, {8,9} and {4,8,12}$ are two such sets. include the empty set in your count.

257

Step-by-step explanation:

The divisors of 72 which are composite number are

4,6,8,9,12,18,36,72 (composite numbers are those numbers which are formed by the multiplication of two whole numbers}

So the total number of divisors which are composite are = 8

So total number of subset

In question it is said that also include empty set in count

So total number of subset =256+1=257

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.