Question

find the value of x.

x = □

Explanation:

Step1: Use the right - angle property

Since \( \angle GHE = 90^{\circ}\), the sum of \(57^{\circ}\) and the angle adjacent to \((3x)^{\circ}\) is \(90^{\circ}\). The adjacent angle to \((3x)^{\circ}\) is \(90 - 57=33^{\circ}\).

Step2: Use the linear - pair property

Angles on a straight line sum to \(180^{\circ}\). So, \(3x+33 = 180\).
Subtract 33 from both sides: \(3x=180 - 33\).
\(3x = 147\).
Divide both sides by 3: \(x=\frac{147}{3}\).

Answer:

\(x = 49\)