Question

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

Explanation:

Step1: Use the property of vertical angles

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

Step2: Solve the equation for \(x\)

Add \(2x\) to both sides of the equation:
\(-2x+2x + 90=x+2x-30\), which simplifies to \(90 = 3x-30\).
Add \(30\) to both sides: \(90 + 30=3x-30 + 30\), so \(120 = 3x\).
Divide both sides by \(3\): \(x=\frac{120}{3}=40\).

Step3: Find \(m\angle D\)

Substitute \(x = 40\) into the expression for \(m\angle D\) (\(m\angle D=x - 30\)).
\(m\angle D=40-30=20\).

Answer:

\(20\)