To find the missing angle measures, we can use the Triangle Sum Theorem, which states that the sum of the angles in a triangle is equal to 180 degrees.
a. The equation to solve for the missing angle measures is:
k + l + j = 180
b. To solve the equation and find the value of x, we substitute the given values for k, l, and j into the equation:
12x + 1 + 16x - 7 + 3x = 180
We combine like terms:
12x + 16x + 3x + 1 - 7 = 180
31x - 6 = 180
Next, we isolate the variable term:
31x = 180 + 6
31x = 186
Finally, we solve for x by dividing both sides of the equation by 31:
x = 186 / 31
x = 6
Therefore, the value of x is 6.