Angle A and angle C are vertical angles. If m∠A = (3x+7) ∘ and m∠C = (x+53) ∘, what is the value of x

Vertical angles are equal

3x+7=x+53

Subtract x from both sides

2x+7=53

Subtract 7 from both sides

2x = 46

X=23

Since it is a given that the angles are vertical, then that means they have to be congruent or = to each other so we can now set up an equation:

3x+7=x+53

Now we need to get the variable alone on one side so subtract 7 from the left (remember what you do, you must do to both sides)

3x=46

Now we can divide by three to get x alone

x=15.333333333 or rounded to 15.33