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The problem presents a triangle with three angles. The measures of these angles are:

- \(40^\circ\),
- \(x^\circ\), 
- \(2x + 11^\circ\).

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

\[
40^\circ + x^\circ + (2x + 11)^\circ = 180^\circ
\]

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

\[
40 + x + 2x + 11 = 180
\]
\[
3x + 51 = 180
\]
\[
3x = 180 - 51
\]
\[
3x = 129
\]
\[
x = \frac{129}{3} = 43
\]

Now that we know \(x = 43^\circ\), we can find the measures of all the angles:

- One angle is \(40^\circ\),
- Another is \(x = 43^\circ\),
- The third angle is \(2x + 11 = 2(43) + 11 = 86 + 11 = 97^\circ\).

Thus, the angles of the triangle are:
- \(40^\circ\),
- \(43^\circ\),
- \(97^\circ\).

Would you like more details on any step?

Here are five related questions:
1. What is the sum of the interior angles of a polygon with more than three sides?
2. How would the solution change if the triangle were a right triangle?
3. Can an interior angle of a triangle ever exceed \(180^\circ\)?
4. How do you find the exterior angles of a triangle?
5. What are some real-life applications of triangle angle properties?

**Tip:** Always remember that in any triangle, the sum of the three angles will always be \(180^\circ\).

Find the value of the variable and the measures of the angles whose degree measure is noted on the figure.

Learn how to find the value of x and the measures of all angles in a triangle where one angle is 40°, another is x°, and the third is (2x + 11)°. This problem uses the triangle angle sum property and basic algebra. Suitable for students in Grades 7-10.

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