Triangle Sum Theorem

Directions: Using the digits 1-9 at most one time each, fill in the blanks so that when you solve for x, it is a whole number.


How many degrees must the two unknown angles sum to?
Can you write an equation to represent the sum of the two unknown angles?


There are many answers. One is:
Top angle is 4x and bottom angle is 6x + 25.
x = 10 solves the problem.

Extension/extra challenge 1: set a value for x and find all the ways to make the problem have that solution.
Extension/extra challenge 2: change the value of the bottom right angle.

Source: Franco D. Adkins

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Systems of Equations 1

Directions: Using the integers -9 to 9 at most one time each, fill in the …


  1. This makes sense for the most part

  2. This kind of makes sense

  3. I understand it

  4. I get it a little still a little confusing.

  5. It’s a little confusing, but for the most part I get it

  6. Can someone explain

  7. Christina Hansson

    The two unknown angles must add up to 125. That is what we know from the triangular theorem, that the sum of all angles must be 180 degrees; thus if we begin with 55, the remainder is 125.
    Any two whole numbers adding up to 125 would be OK, only, one is represented ’_x+__’, which means that there is a double digit number next to the ’x part’.
    If we try to use too large or small numbers for our x, we cannot get double digits.
    63+62=125 could come from x=9, ie 7x+(6x+8) but 8 is only one digit.
    Also, many examples could leave us with no extra number:
    100+25=125 could have been ok but that addition could mean x=25 and 4x+x=125 and no extra number.
    But try 50+75 and use x=10:
    50+75=125 and then 5x+(6x+15), which is ok!
    [We have to think of 75 as being 6x+15 even though it could also be written as 7x+5, but then we see a single digit again and that is not ok.]

  8. Has anyone tried this with their kids? I would love to know how the lesson went!

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