a. Write an equation that would help you solve for the missing angle measures. Combine Like Terms! Remember the Triangle Sum Theorem.
b. Solve the equation to find the value of x. Show/Explain all of your steps using inverse operations! (2 points)
k=12x+1
l=16x-7
j=3x
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.