if angles 1 and 2 are a linear pair, and m<1 = 3x + 12 and m<2 = x + 44, find the measures of these two angles
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Given that angles 1 and 2 form a linear pair, we know that their measures add up to 180 degrees.
So we can set up the equation:
m<1 + m<2 = 180
(3x + 12) + (x + 44) = 180
Combining like terms:
4x + 56 = 180
Subtracting 56 from both sides:
4x = 180 - 56
4x = 124
Dividing both sides by 4:
x = 124/4
x = 31
Now we can substitute this value of x back into the original expressions to find the measures of angles 1 and 2:
m<1 = 3x + 12 = 3(31) + 12 = 93 + 12 = 105
m<2 = x + 44 = 31 + 44 = 75
Therefore, angle 1 measures 105 degrees and angle 2 measures 75 degrees.