To solve for $x$, we will use the property of triangles that the sum of the measures of the angles in a triangle is $180^\circ$.

Step 1: Express the angles

• Angle $A = x + 4$
• Angle $B = 2 \cdot \text{Angle A} = 2(x + 4)$
• Angle $C = \text{Angle B} = 2(x + 4)$

Step 2: Write the equation

The sum of the angles is: $\text{Angle A} + \text{Angle B} + \text{Angle C} = 180$ Substitute the expressions for each angle: $(x + 4) + 2(x + 4) + 2(x + 4) = 180$

Step 3: Simplify the equation

Expand each term: $x + 4 + 2x + 8 + 2x + 8 = 180$ Combine like terms: $5x + 20 = 180$

Step 4: Solve for $x$

Subtract 20 from both sides: $5x = 160$ Divide by 5: $x = 32$

Final Answer:

$x = 32$

Verification:

• Angle $A = x + 4 = 32 + 4 = 36^\circ$
• Angle $B = 2 \cdot 36 = 72^\circ$
• Angle $C = 72^\circ$
• Sum of the angles: $36 + 72 + 72 = 180$, which confirms the solution is correct.

Let me know if you'd like further clarification or have any questions!

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Five related questions:

1. What is the measure of each angle in the triangle after solving for $x$?
2. How would the problem change if angle $C$ was not equal to angle $B$?
3. Can a triangle have two equal angles if $x$ is negative?
4. How do you derive the formula for the sum of the angles in a triangle?
5. What types of triangles can this problem represent based on the given angle relations?

Tip: Always double-check your solution by substituting it back into the original equations to verify the results.