Question

Prove x = 8 if the m<ADC = 54 degrees

m<ADB + m<BDC = m<ADC: _____

3x-2+4x=54: ______

7x - 2 = 54: Simplifying

7x = 56: ______

x = 8: ______

Answer 1

If you're being asked what rules/steps go in the blanks for the proof:
Blank 1) Adding adjacent angles
I'm guessing 54° is the angle measurement of ∠ADC. You know the measurements of ∠ADB = (3x-2)° and ∠BDC = (4x)°. Since those two angles are adjacent angles, meaning they share the same side B and the same endpoint D, they can be added together to create a larger angle, ∠ADC, that is the sum of both their angles.

Blank 2) Isolating the variable
You are adding 2 to both sides of the equation to isolate the 7x.

Blank 3) Solving for x
You are dividing both sides by 7 to get the value of x.