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Arturiano [62]
2 years ago
7

What is the value of k ?

Mathematics
2 answers:
never [62]2 years ago
4 0

Answer:

27°

Step-by-step explanation:

Remember the angle opposite of another angle in two straight lines are equal

So 66=39+k

Then put k by itself by subtracting 39 from both sides

66-39=k

k=27°

liubo4ka [24]2 years ago
3 0

Answer:

27-degrees

Step-by-step explanation:

these are vertical angles which are equal to each other *congruent

39 + k = 66 --> *subtract 39 from both sides*

k = 27

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Answer:

I'm going to paint you a picture in words of what this looks like on paper.  We have a train leaving from a point on your paper heading straight west.  We have another train leaving from the same point on your paper heading straight east.  This is the "opposite directions" that your problem gives you.  

Now let's make a table:

                distance       =        rate      *       time

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We will fill in this table from the info in the problem then refer back to our drawing.  It says that one train is traveling 12 mph faster than the other train.  We don't know how fast "the other train" is going, so let's call that rate r.  If the first train is travelin 12 mph faster, that rate is r + 12.  Let's put that into the table

              distance        =        rate        *        time

Train 1                                        r

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Then it says "after 2 hours", so the time for both trains is 2 hours:

         

              distance        =        rate        *        time

Train 1                                        r           *          2

Train 2                                  (r + 12)       *          2

Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r.  The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24.  The distance between them (which is also the length of the whole entire arrow) is 232.  Thus:

2r + 2r + 24 = 232 and

4r = 208 so

r = 52

This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph

Step-by-step explanation:

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