In preparation for a conference, Derek is setting up some stations where people can create their own name tags. He has 10 name tags and 18 pens, which he wants to distribute evenly among the name tag stations with none left over. What is the greatest number of name tag stations that Derek can set up?

2

Step-by-step explanation:

Given that:

Number of name tags = 10

Number of pens = 18

to distribute evenly among the name tag stations with none left over ; we need to obtain the greatest common factors of both 10 and 18 to know the number of stations Derek can set up ;

Factors of :

10 : 1, 2, 5, 10

18 : 1, 2, 3, 6, 9, 18

The greatest common factor is 2.

Hence, Derek can setup 2 stations.

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db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)