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We are given a triangle with angle measures expressed in terms of \( x \):

- \( \angle A = x \)
- \( \angle B = 12x \)
- \( \angle C = 5x \)

In any triangle, the sum of the interior angles is always \( 180^\circ \). Therefore, we can set up the equation:

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

Substituting the given expressions for the angles:

\[
x + 12x + 5x = 180
\]

Simplifying:

\[
18x = 180
\]

Solving for \( x \):

\[
x = \frac{180}{18} = 10
\]

Thus, \( x = 10^\circ \).

Therefore, the measure of angle \( A \) is \( \boxed{10^\circ} \).

Would you like more details, or do you have any further questions?

Here are 5 related questions to expand your knowledge:
1. What is the measure of angle \( B \)?
2. How do you determine the sum of interior angles in polygons other than triangles?
3. What would happen if one of the angle expressions was negative?
4. How can you use the Law of Sines in a triangle with angles given like this?
5. What are the properties of similar triangles?

**Tip**: Always remember, in any triangle, the sum of the three angles is \( 180^\circ \), which is a key fact for solving problems involving unknown angles.

The measures of the angles of the triangle are indicated in terms of x. Find the measure of angle A, given that angle A = x, angle B = 12x, and angle C = 5x.

Learn how to solve for angle A in a triangle where the angles are given as x, 12x, and 5x. Using the triangle angle sum theorem, this problem walks through how to determine the unknown angle. Suitable for students in Grades 7-9.

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