Question

if \\( \triangle g h j \\) is isosceles, find the value of \\( x \\).

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle, the base angles are equal. The sum of angles in a triangle is \(180^{\circ}\). Let the two equal - side - opposite angles be considered. If \(\triangle GHJ\) has two equal sides (marked), then the angles opposite to those sides are equal. Let \(\angle H=\angle J=(14x + 1)^{\circ}\), and \(\angle G = 38^{\circ}\).
So, \(38+(14x + 1)+(14x + 1)=180\).

Step2: Simplify the equation

First, combine like terms:

$$
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$$

Then, subtract 40 from both sides: \(28x=180 - 40\), so \(28x=140\).

Step3: Solve for \(x\)

Divide both sides of the equation \(28x = 140\) by 28: \(x=\frac{140}{28}\).

Answer:

\(x = 5\)