Question

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!

Answer 1

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.