Question

question
in $\triangle lmn$, $m\angle l = (4x - 4)\degree$, $m\angle m = (x - 8)\degree$, and $m\angle n = (6x - 6)\degree$. find $m\angle n$.

Explanation:

Step1: Use the triangle angle - sum theorem

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

Step2: Simplify the left - hand side of the equation

Combine like terms: \((4x+x + 6x)+(-4-8 - 6)=180\).
\(11x-18 = 180\).

Step3: Solve for \(x\)

Add \(18\) to both sides of the equation: \(11x-18 + 18=180 + 18\).
\(11x=198\).
Divide both sides by \(11\): \(x=\frac{198}{11}=18\).

Step4: Find \(m\angle N\)

Substitute \(x = 18\) into the expression for \(m\angle N\): \(m\angle N=(6x - 6)^{\circ}\).
\(m\angle N=(6\times18-6)^{\circ}=(108 - 6)^{\circ}\).

Answer:

\(102^{\circ}\)