https://file.aiquickdraw.com/mathbot/file/1726138754732t4ktb8kx.jpg

The diagram in the image represents a right triangle where one of the angles is \( \angle a \), the other is \( \angle b \), and the third is a right angle (90 degrees).

From the diagram:
- \( \angle a = x + 4 \)
- \( \angle b = 3x + 2 \)
- The right angle is 90 degrees.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the following equation:

\[
(x + 4) + (3x + 2) + 90 = 180
\]

Now, let's solve for \( x \):

\[
x + 4 + 3x + 2 + 90 = 180
\]

\[
4x + 96 = 180
\]

\[
4x = 180 - 96
\]

\[
4x = 84
\]

\[
x = \frac{84}{4} = 21
\]

So, the value of \( x \) is \( \boxed{21} \).

Would you like any further details or have any questions?

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Here are some related questions to expand your understanding:
1. How do you calculate the sum of angles in any triangle?
2. If \( x = 21 \), what are the values of \( \angle a \) and \( \angle b \)?
3. Can you explain why the angles of any triangle must sum to 180 degrees?
4. How would the solution change if the given angles were not part of a right triangle?
5. What is the difference between solving for \( x \) in geometric problems versus algebraic problems?

**Tip:** Always remember that in any triangle, the sum of the angles is 180 degrees, and this fact can be used to solve for unknown variables involving angles.

Find the value of x given two angles: angle a = x + 4 and angle b = 3x + 2 in a right triangle.

This problem involves finding the value of x in a right triangle, where angle a is x + 4, angle b is 3x + 2, and the third angle is 90 degrees. The solution involves using the angle sum property of triangles.

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