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.(2 points) m<1 = degrees m<2 = degrees
Since angles 1 and 2 are a linear pair, their measures add up to 180 degrees.
Therefore, we can set up the equation:
m<1 + m<2 = 180 degrees
Substituting the given expressions for the measures of the angles:
3x + 12 + x + 44 = 180
Combining like terms:
4x + 56 = 180
Subtracting 56 from both sides:
4x = 124
Dividing both sides by 4:
x = 31
Now, we can substitute the value of x back into the expressions for the angles' measures:
m<1 = 3(31) + 12 = 93 + 12 = 105 degrees
m<2 = 31 + 44 = 75 degrees
Therefore, m<1 = 105 degrees and m<2 = 75 degrees.