https://file.aiquickdraw.com/mathbot/file/1727237490938txq9oje5.jpg

The image shows a triangle with angle measures indicated in terms of \(x\). Specifically:

- \(\angle A = 4x - 10\)
- \(\angle B = x\)
- \(\angle C = x + 16\)

To find the measure of \(\angle A\), we will use the fact that the sum of the interior angles of a triangle is always 180 degrees. Therefore, the equation is:

\[
(4x - 10) + x + (x + 16) = 180
\]

Let me solve this equation step by step.

1. Combine like terms:
\[
6x + 6 = 180
\]

2. Subtract 6 from both sides:
\[
6x = 174
\]

3. Divide by 6:
\[
x = 29
\]

Now that we know \(x = 29\), we can substitute this value back into the expression for \(\angle A\):

\[
\angle A = 4x - 10 = 4(29) - 10 = 116 - 10 = 106^\circ
\]

Thus, the measure of \(\angle A\) is \(106^\circ\).

Would you like further explanation or details?

### Related Questions:
1. How can you find the measures of \(\angle B\) and \(\angle C\)?
2. Why does the sum of the angles in a triangle always equal 180 degrees?
3. What types of triangles exist based on angle measures?
4. How would the equation change if the triangle was not a right triangle?
5. Can you classify this triangle based on the given angle measures?

### Tip:
Always check the sum of your angle measures when working with triangles to ensure they add up to 180°.

The measures of the angles of the triangle are indicated in terms of x. Find the measure of angle A.

Find the measure of angle A in a triangle where the angles are expressed in terms of x. The problem involves algebraic manipulation and using the sum of angles theorem. Suitable for Grades 7-9 students learning triangle geometry and algebra.

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