To solve for \( x \) in the problem provided, we need to set up an equation based on the measures of the angles in a triangle. The sum of the angles in a triangle is always \( 180^\circ \).
Let’s define the angles based on the information given:
- The measure of angle \( A \) is \( x + 4 \).
- The measure of angle \( B \) is twice the measure of angle \( A \), so \( B = 2(x + 4) \).
- The measure of angle \( C \) is equal to the measure of angle \( B \), so \( C = 2(x + 4) \).
Now, we can express the sum of the angles:
\[ A + B + C = 180^\circ \]
Substituting the expressions for \( A \), \( B \), and \( C \):
\[ (x + 4) + 2(x + 4) + 2(x + 4) = 180 \]
Now, simplify the equation:
\[ (x + 4) + 2x + 8 + 2x + 8 = 180 \]
Combine like terms:
\[ x + 2x + 2x + 4 + 8 + 8 = 180 \] \[ 5x + 20 = 180 \]
Next, isolate \( x \) by subtracting 20 from both sides:
\[ 5x = 160 \]
Now, divide by 5:
\[ x = 32 \]
Thus, the value of \( x \) is \( \boxed{32} \).
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