Vertical angles are congruent to each other because of the vertical angles theorem. This theorem states that vertical angles are congruent.
Since we know that ∠C and ∠D must be congruent to each other, make them equal to each other in an equation.
m∠C = m∠D
-3x + 58 = x - 2
- Add 3x to both sides of the equation.
58 = 4x - 2
- Add 2 to both sides of the equation.
60 = 4x
- Divide both sides of the equation by 4.
15 = x, or x = 15
- Now substitute what we found for x (15) into m∠D.
m∠D = (15) - 2
m∠D = 13°
