∠C and ∠D are vertical angles with m∠C=−3x+58 and m∠D=x−2. What is m∠D? Enter your answer in the box. °

Step-by-step explanation:

By the vertical angle theorem, we know that the measures of angles C and D are equivalent. From this, we can create an equation and then solve for the value of x. So we create: x-2 = -3x+58, which simplifies to 4x = 60. Now we divide both sides by 4, to get x = 15. We can substitute this value into x-2 to get the angle measure of D. So we get (15)-2 = m∠D and this simplifies to 13° =  m∠D.