Question

calculator what is ( mangle dhg )? enter your answer in the box. ( square^{circ} )

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(6(x - 2)=3x + 30\).

Step2: Solve the equation for \(x\)

Expand \(6(x - 2)\) to get \(6x-12\). The equation becomes \(6x-12 = 3x + 30\).
Subtract \(3x\) from both sides: \(6x-3x-12=3x - 3x+ 30\), which simplifies to \(3x-12 = 30\).
Add \(12\) to both sides: \(3x-12 + 12=30 + 12\), so \(3x=42\).
Divide both sides by \(3\): \(x=\frac{42}{3}=14\).

Step3: Find \(m\angle DHG\)

Substitute \(x = 14\) into \(6(x - 2)\).
\(6(14 - 2)=6\times12 = 108\).

Answer:

\(108\)