Question

what is the value of x? x - 36° f e g x = °

Explanation:

Step1: Identify isosceles - triangle property

Since the two line - segments with the red marks are equal, $\triangle FEG$ is isosceles and the base - angles are equal. So the other base - angle is also $x - 36^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $(x - 36^{\circ})+(x - 36^{\circ})+x=180^{\circ}$.

Step3: Simplify the equation

Combine like terms: $3x-72^{\circ}=180^{\circ}$.

Step4: Solve for x

Add $72^{\circ}$ to both sides: $3x=180^{\circ}+72^{\circ}=252^{\circ}$. Then divide both sides by 3: $x = 84^{\circ}$.

Answer:

$84$