In ΔTUV, m, angle, T, equals, left parenthesis, 5, x, minus, 3, right parenthesis, degreesm∠T=(5x−3) 
∘
 , m, angle, U, equals, left parenthesis, 4, x, plus, 4, right parenthesis, degreesm∠U=(4x+4) 
∘
 , and m, angle, V, equals, left parenthesis, x, minus, 11, right parenthesis, degreesm∠V=(x−11) 
∘
 . Find m, angle, V, .m∠V.

To find the measure of angle \( V \) (denoted as \( m\angle V \)) in triangle \( \Delta TUV \), we can use the fact that the sum of the angles in any triangle is always \( 180^\circ \). So, we have the equation:

\[
m\angle T + m\angle U + m\angle V = 180^\circ
\]

The given values are:
\[
m\angle T = (5x - 3)^\circ, \quad m\angle U = (4x + 4)^\circ, \quad m\angle V = (x - 11)^\circ
\]

Substitute these into the equation:

\[
(5x - 3) + (4x + 4) + (x - 11) = 180
\]

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

### Step 1: Combine like terms
\[
5x + 4x + x - 3 + 4 - 11 = 180
\]
\[
10x - 10 = 180
\]

### Step 2: Solve for \( x \)
\[
10x = 190
\]
\[
x = 19
\]

### Step 3: Find \( m\angle V \)
Now that we know \( x = 19 \), substitute it back into the expression for \( m\angle V = (x - 11) \):

\[
m\angle V = 19 - 11 = 8^\circ
\]

Thus, \( m\angle V = 8^\circ \).

Let me know if you need further details or have any questions. Here are some related questions for further practice:

1. What is the measure of \( m\angle T \) when \( x = 19 \)?
2. What is the measure of \( m\angle U \) when \( x = 19 \)?
3. Can the angles in a triangle ever sum to more than \( 180^\circ \)?
4. If \( \Delta ABC \) has angles represented similarly, how would you solve for unknown angles?
5. What is the significance of a triangle's angle sum theorem in geometry?

**Tip:** Always remember to check if the sum of your angles equals \( 180^\circ \) when solving for unknowns in triangles.

In ΔTUV, m∠T = (5x − 3)°, m∠U = (4x + 4)°, and m∠V = (x − 11)°. Find m∠V.

Learn how to solve for the unknown angle m∠V in triangle ΔTUV using algebra and the Triangle Angle Sum Theorem. This problem involves key concepts in geometry and algebra and provides a step-by-step solution, suitable for students in Grades 8-10.

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