To solve for \( x \) given the measures of the angles of the triangle, we need to set up the expressions based on the information provided:
- The measure of angle A is \( A = x + 4 \) degrees.
- The measure of angle B is twice the measure of angle A, so \( B = 2A = 2(x + 4) = 2x + 8 \) degrees.
- The measure of angle C is equal to the measure of angle B, so \( C = B = 2x + 8 \) degrees.
According to the triangle angle sum theorem, the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:
\[ A + B + C = 180 \]
Substituting the expressions for angles A, B, and C into the equation:
\[ (x + 4) + (2x + 8) + (2x + 8) = 180 \]
Now, combine the terms:
\[ x + 4 + 2x + 8 + 2x + 8 = 180 \]
This simplifies to:
\[ 5x + 20 = 180 \]
Next, isolate \( x \) by subtracting 20 from both sides:
\[ 5x = 160 \]
Now, divide by 5:
\[ x = 32 \]
Thus, the value of \( x \) is \( \boxed{32} \).