Math Problem Statement
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.
Solution
To find the measure of angle (denoted as ) in triangle , we can use the fact that the sum of the angles in any triangle is always . So, we have the equation:
The given values are:
Substitute these into the equation:
Now, let's solve for :
Step 1: Combine like terms
Step 2: Solve for
Step 3: Find
Now that we know , substitute it back into the expression for :
Thus, .
Let me know if you need further details or have any questions. Here are some related questions for further practice:
- What is the measure of when ?
- What is the measure of when ?
- Can the angles in a triangle ever sum to more than ?
- If has angles represented similarly, how would you solve for unknown angles?
- 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 when solving for unknowns in triangles.
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Math Problem Analysis
Mathematical Concepts
Algebra
Geometry
Triangle Angle Sum
Formulas
Sum of angles in a triangle: m∠T + m∠U + m∠V = 180°
Theorems
Triangle Angle Sum Theorem
Suitable Grade Level
Grades 8-10