https://file.aiquickdraw.com/mathbot/file/1729144861488liyh1fei.jpg

To solve for \( x \) in this triangle, we can apply the fact that the sum of the interior angles of any triangle is always \( 180^\circ \).

In the image, the triangle has three angles:
1. One right angle (\( 90^\circ \)),
2. Another angle given as \( 23^\circ \),
3. The remaining angle is \( (8x + 3)^\circ \).

### Step-by-step solution:

The sum of the interior angles of the triangle is:
\[
90^\circ + 23^\circ + (8x + 3)^\circ = 180^\circ
\]

Simplifying this:
\[
113^\circ + (8x + 3)^\circ = 180^\circ
\]
\[
116^\circ + 8x = 180^\circ
\]
Now, subtract \( 116^\circ \) from both sides:
\[
8x = 180^\circ - 116^\circ
\]
\[
8x = 64^\circ
\]
Finally, divide both sides by 8 to solve for \( x \):
\[
x = \frac{64}{8} = 8
\]

Thus, the value of \( x \) is \( \boxed{8} \).

Let me know if you need more details or have any questions!

Here are 5 related questions for practice:
1. If one of the angles of a triangle is \( 40^\circ \) and another is \( 60^\circ \), what is the third angle?
2. In a right triangle, if one of the acute angles is \( 30^\circ \), what is the other acute angle?
3. If the expression for an angle of a triangle is \( 5x + 10 \), how do you find \( x \)?
4. What is the sum of the exterior angles of a triangle?
5. How does the Pythagorean theorem apply to a right triangle like the one shown?

### Tip:
Always double-check the angle sum in a triangle—it should always be \( 180^\circ \)!

The measures of the angles of a triangle are shown in the figure below. Solve for x. The triangle has a right angle, an angle of 23°, and the third angle is represented as (8x + 3)°.

Learn how to solve for x in a triangle problem involving a right angle, an angle of 23°, and the third angle expressed as (8x + 3)°. This solution uses the Interior Angle Sum Theorem and basic algebra to find x.

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