https://file.aiquickdraw.com/mathbot/file/1725977145733qvc7nk2k.jpg

To solve for \( x \) in the triangle given in the image, we can apply the property that the sum of the interior angles in any triangle is always 180°.

From the image, the three angles of the triangle are:

1. \( (x + 15)^\circ \) at vertex \( A \),
2. \( (2x + 1)^\circ \) at vertex \( B \),
3. \( x^\circ \) at vertex \( C \).

Thus, the equation becomes:
\[
(x + 15) + (2x + 1) + x = 180
\]
Now let's solve for \( x \).

\[
x + 15 + 2x + 1 + x = 180
\]

Combine like terms:

\[
4x + 16 = 180
\]

Subtract 16 from both sides:

\[
4x = 164
\]

Now divide both sides by 4:

\[
x = 41
\]

Thus, \( x = 41 \).

Would you like a detailed explanation on the next steps or additional clarifications?

Here are 5 related questions for further exploration:
1. What are the actual measures of all the angles in this triangle once \( x = 41 \)?
2. How would you check if the triangle is an acute, right, or obtuse triangle?
3. Can you apply the Law of Sines to this triangle if any side lengths are given?
4. What changes if one of the angles was an exterior angle instead of interior?
5. How would the approach change if the sum of angles wasn't known?

**Tip:** Always check the sum of your angles in a triangle to ensure accuracy—it should always total 180°!

Given the triangle with angles (x + 15)°, (2x + 1)°, and x°, solve for x.

This problem demonstrates how to solve for x in a triangle with angles (x + 15)°, (2x + 1)°, and x°. Learn how to apply the sum of angles in a triangle theorem to find the value of x. Suitable for students in Grades 8-10.

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