Question

find the value of x.

Explanation:

Step1: Use the property of right - angle

Since \( \angle FHG = 57^{\circ}\) and \( \angle GHD = 90^{\circ}\), and the sum of \(57^{\circ}\) and \((3x)^{\circ}\) is \(90^{\circ}\) (because they are complementary angles). So we get the equation \(57 + 3x=90\).

Step2: Solve the equation for \(x\)

Subtract \(57\) from both sides of the equation \(57 + 3x=90\).
\(3x=90 - 57\)
\(3x = 33\)
Divide both sides by \(3\): \(x=\frac{33}{3}\)

Answer:

\(11\)