Question

∠c and ∠d are vertical angles with ( mangle c=-2x + 90 ) and ( mangle d=x - 30 ). what is ( mangle d )? enter your answer in the box.

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(m\angle C = m\angle D\).
\(-2x + 90=x - 30\)

Step2: Solve for \(x\)

Add \(2x\) to both sides:
\(90 = 3x-30\)
Add \(30\) to both sides:
\(120 = 3x\)
Divide both sides by \(3\):
\(x = 40\)

Step3: Find \(m\angle D\)

Substitute \(x = 40\) into \(m\angle D=x - 30\)
\(m\angle D=40 - 30\)

Answer:

\(10\)