A triangle has three angles: angle K=(12x + 1), angle J=(3x), and angle L=(16x - 7)
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 ×. Show/Explain all of your steps using inverse operations!
a. The Triangle Sum Theorem states that the sum of all angles in a triangle is equal to 180 degrees. Therefore, we can set up the equation:
angle K + angle J + angle L = 180
(12x + 1) + (3x) + (16x - 7) = 180
b. Now, let's solve the equation using inverse operations:
Combine like terms:
12x + 1 + 3x + 16x - 7 = 180
31x - 6 = 180
Add 6 to both sides to isolate the variable:
31x - 6 + 6 = 180 + 6
31x = 186
Divide both sides by 31 to solve for x:
31x/31 = 186/31
x = 6
Therefore, the value of x is 6.