Question

∠C and ​ ∠D ​ are vertical angles with m∠C=−2x+90 and m∠D=x−30

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What is m∠D
?

Answer 1

Vertical angle are equal:
m∠C = m∠D
−2x+90 = x−30
Add 2x to both sides:
90 = 3x - 30
Add 30 to both side:
120 = 3x
Divide both sides by 3:
x = 40
Plugging in:
m∠D=x−30 = 40-30 = 10

The answer is m∠D = 10

Answer 2

As they are vertical angles, their magnitude will be equal.
-2x+90 = x-30
2x+x = 90+30
3x = 120
x = 120/3
x = 40

Now, m∠D = x-30 = 40-30 = 10

So, Your Final Answer would be 10 degrees.

Hope this helps!