In ΔBCD, m, angle, B, equals, left parenthesis, 8, x, plus, 13, right parenthesis, degreesm∠B=(8x+13) 
∘
 , m, angle, C, equals, left parenthesis, 2, x, plus, 13, right parenthesis, degreesm∠C=(2x+13) 
∘
 , and m, angle, D, equals, left parenthesis, x, plus, 11, right parenthesis, degreesm∠D=(x+11) 
∘
 . What is the value of x, question markx?

In a triangle, the sum of the interior angles is always \(180^\circ\). Therefore, for triangle \( \Delta BCD \), we can write the following equation for the sum of the angles:

\[
m\angle B + m\angle C + m\angle D = 180^\circ
\]

Substitute the given expressions for the angles:

\[
(8x + 13) + (2x + 13) + (x + 11) = 180
\]

Now, combine like terms:

\[
8x + 2x + x + 13 + 13 + 11 = 180
\]
\[
11x + 37 = 180
\]

Subtract 37 from both sides:

\[
11x = 143
\]

Now, divide by 11:

\[
x = \frac{143}{11} = 13
\]

Thus, the value of \(x\) is:

\[
x = 13
\]

Would you like a breakdown of the steps, or do you have any other questions?

### Related Questions:
1. What are the measures of angles \( \angle B \), \( \angle C \), and \( \angle D \) after finding \(x\)?
2. How would the solution change if one of the angles was given as an exterior angle?
3. Can the same approach be used for non-triangular polygons? Why or why not?
4. How do you solve similar problems for an isosceles or equilateral triangle?
5. What happens if one of the angles was expressed as a quadratic function of \(x\)?

### Tip:
Always remember that the sum of the interior angles of any triangle is \(180^\circ\), which is a fundamental rule in geometry.

In ΔBCD, m∠B=(8x+13)°, m∠C=(2x+13)°, and m∠D=(x+11)°. What is the value of x?

Learn how to solve for x in triangle ΔBCD with angle measures given as (8x+13)°, (2x+13)°, and (x+11)°. This solution applies the Triangle Angle Sum Theorem, combining algebraic concepts and angle relationships. Suitable for students in Grades 7-9.

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