Question

question
in ( \triangle t u v, m angle t=(4 x-4)^{circ}, m angle u=(6 x+8)^{circ} ), and ( m angle v=(x+11)^{circ} ). find ( m angle v ).
answer attempt 1 out of 2
( m angle v=\frac{1}{square} ) ( circ )
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Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(m\angle T + m\angle U + m\angle V=180^{\circ}\).
Substitute the given expressions: \((4x - 4)+(6x + 8)+(x + 11)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((4x+6x + x)+(-4 + 8+11)=180\).
\(11x+15 = 180\).

Step3: Solve for \(x\)

Subtract 15 from both sides: \(11x=180 - 15\).
\(11x=165\).
Divide both sides by 11: \(x=\frac{165}{11}=15\).

Step4: Find \(m\angle V\)

Substitute \(x = 15\) into the expression for \(m\angle V\).
\(m\angle V=x + 11\).
\(m\angle V=15+11\).

Answer:

\(26\)