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The problem you're working on involves a triangle \( \triangle ABC \), where \( \angle B = \angle C \). You are given the expressions for angles \( \angle B \) and \( \angle C \) in terms of \( x \), specifically:

\[
\angle B = 2x + 47^\circ \quad \text{and} \quad \angle C = 9x + 33^\circ
\]

Since \( \angle B = \angle C \), we can set the two expressions equal to each other and solve for \( x \).

\[
2x + 47 = 9x + 33
\]

Let's solve this equation.

### Step-by-step solution:
1. Subtract \( 2x \) from both sides:
\[
47 = 7x + 33
\]
2. Subtract 33 from both sides:
\[
14 = 7x
\]
3. Divide both sides by 7:
\[
x = 2
\]

Now that we know \( x = 2 \), we can substitute this value back into the expressions for \( \angle B \) and \( \angle C \).

\[
\angle B = 2(2) + 47 = 4 + 47 = 51^\circ
\]
\[
\angle C = 9(2) + 33 = 18 + 33 = 51^\circ
\]

Therefore, both \( \angle B \) and \( \angle C \) measure \( 51^\circ \).

Since the sum of the angles in any triangle is \( 180^\circ \), we can now find \( \angle A \):

\[
\angle A = 180^\circ - 51^\circ - 51^\circ = 78^\circ
\]

So, the measure of \( \angle A \) is \( 78^\circ \).

Would you like more details on any of the steps? Here are five follow-up questions that could expand your understanding of this topic:

1. How can we verify that the sum of angles in a triangle is always \( 180^\circ \)?
2. If \( \angle B \neq \angle C \), how would the approach change?
3. What are some other properties of isosceles triangles, like the one in this problem?
4. How do these angle equations relate to the interior and exterior angles of polygons?
5. How would the solution change if the triangle was not isosceles?

### Tip:
Always check your work by confirming that the sum of all angles in the triangle adds up to \( 180^\circ \).

When viewed from the side, the spire on the top of a building forms triangle \(\triangle ABC\) with \(\angle B = \angle C\). What is the measure of \(\angle B\)?

Learn how to determine the angles of an isosceles triangle formed by a building spire with given algebraic expressions. This solution explains how to solve for \(x\) and find the measures of \(\angle B\) and \(\angle C\). Suitable for students in Grades 7-10.

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