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The diagram shows an isosceles triangle \( \triangle ABC \), where \( AB = AC \). The measure of angle \( A \), denoted as \( m\angle A \), is given by \( (4x + 28)^\circ \). Since \( \triangle ABC \) is isosceles, the two base angles, \( \angle B \) and \( \angle C \), are congruent.

We know that the sum of the angles in any triangle is \( 180^\circ \). Let the measure of angles \( B \) and \( C \) each be \( \theta \). Therefore, we have the equation:

\[
m\angle A + m\angle B + m\angle C = 180^\circ
\]

Since \( m\angle B = m\angle C = \theta \), the equation becomes:

\[
(4x + 28) + 2\theta = 180
\]

Now, solve for \( \theta \):

\[
2\theta = 180 - (4x + 28)
\]
\[
2\theta = 152 - 4x
\]
\[
\theta = \frac{152 - 4x}{2} = 76 - 2x
\]

Since \( \theta \) represents the base angles \( B \) and \( C \), we now have an expression for these angles in terms of \( x \).

Let me know if you'd like me to continue solving for \( x \) or if you need clarification on any steps so far. 

Here are 5 follow-up questions related to this problem:

1. How do we derive the sum of interior angles of any triangle?
2. What property of isosceles triangles makes \( \angle B \) and \( \angle C \) equal?
3. How can we verify that the equation setup for solving \( x \) is correct?
4. What happens to the values of the angles when \( x \) is increased?
5. How would the problem change if it were not an isosceles triangle?

**Tip:** In any triangle, identifying congruent angles can simplify the calculation of unknown values using symmetry properties.

Find the value of x given that m∠A = (4x + 28)° in an isosceles triangle where AB = AC.

Solve for x in an isosceles triangle where angle A is given as (4x + 28)° and base angles are congruent. This problem demonstrates the application of the Isosceles Triangle Theorem and the Sum of Interior Angles Theorem, suitable for students in Grades 8-10.

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