Final answer:
Vertical angles ∠C and ∠D are equal in measure, and by setting their expressions equal and solving for x, we determine that none of the provided choices match the measure of ∠D, which is calculated to be 10°. the measure of angle D is x - 30
Step-by-step explanation:
The student has asked how to find the measure of ∠D given that ∠C and ∠D are vertical angles with m∠C = -2x + 90 and m∠D = x - 30. Since vertical angles are congruent, their measures are equal. Thus, we can set the expressions for their measures equal to each other to solve for x:
2x + 90 = x - 30
Adding 2x to both sides gives us 90 = 3x - 30. Adding 30 to both sides yields 120 = 3x. Dividing both sides by 3 gives us x = 40. Now we substitute x back into the expression for m∠D:
m∠D = (40) - 30 = 10
None of the provided choices (A) x + 30, (B) 90 - 2x, (C) 2x - 30, (D) 30 - x match the correct answer, meaning there seems to be an error either in the problem statement or the provided choices.To find the measure of angle D, we can set the measure of angle C equal to the measure of angle D, as they are vertical angles. So, we have the equation -2x + 90 = x - 30.
By solving this equation, we can find the value of x. Then, we can substitute the value of x back into the expression for angle D, which is x - 30, to find the measure of angle D.
So, the measure of angle D is x - 30