a. The Triangle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees. So, we can write the equation:
J + K + L = 180
b. Let's substitute the expressions for J, K, and L into the equation:
3x + (12x + 1) + (16x - 7) = 180
Now, let's combine like terms:
3x + 12x + 1 + 16x - 7 = 180
31x - 6 = 180
Next, let's isolate the variable x by adding 6 to both sides of the equation:
31x - 6 + 6 = 180 + 6
31x = 186
Finally, let's solve for x by dividing both sides of the equation by 31:
31x/31 = 186/31
x = 6
So, the value of x is 6.