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a. To find the missing angle measures, we can use the Triangle Sum Theorem. The theorem states that the sum of the interior angles in a triangle is always 180 degrees.
Let's denote the missing angle measure as m. The equation to solve for the missing angle measure would be:
k + l + j + m = 180
Substituting the given expressions for k, l, and j, we have:
(12x + 1) + (16x - 7) + (3x) + m = 180
Now, let's combine like terms.
12x + 16x + 3x + 1 - 7 + m = 180
31x - 6 + m = 180
b. To solve for x, we can isolate the x-term.
31x = 180 - m + 6
31x = 186 - m
Divide both sides by 31:
x = (186 - m)/31
Thus, the value of x is (186 - m)/31.