Question

solve for the variable.
x = type your answer...

Explanation:

Step1: Identify triangle type

Triangle \( EHG \) is isosceles right triangle (legs \( EH = GH \), right angle at \( H \)). So base angles are equal and each is \( 45^\circ \).

Step2: Set up equation

Given \( \angle G=(3x + 6)^\circ \), and in isosceles right triangle, non - right angles are \( 45^\circ \). So \( 3x+6 = 45 \).

Step3: Solve for \( x \)

Subtract 6 from both sides: \( 3x=45 - 6=39 \).
Divide both sides by 3: \( x=\frac{39}{3}=13 \).

Answer:

\( x = 13 \)