Question

in the triangle below, suppose that $m\angle l=(2x - 5)\degree$, $m\angle m=(6x - 4)\degree$, and $m\angle n=x\degree$.
find the degree measure of each angle in the triangle.
$m\angle l=\square\degree$
$m\angle m=\square\degree$
$m\angle n=\square\degree$

Explanation:

Step1: Sum of angles in triangle

The sum of the interior angles of a triangle is \( 180^\circ \). So, we set up the equation: \( (2x - 5) + (6x - 4) + x = 180 \).

Step2: Combine like terms

Combine the \( x \)-terms and the constant terms: \( 2x + 6x + x - 5 - 4 = 180 \), which simplifies to \( 9x - 9 = 180 \).

Step3: Solve for \( x \)

Add 9 to both sides: \( 9x = 180 + 9 = 189 \). Then divide both sides by 9: \( x = \frac{189}{9} = 21 \).

Step4: Find each angle

• For \( \angle L \): Substitute \( x = 21 \) into \( 2x - 5 \): \( 2(21) - 5 = 42 - 5 = 37 \).
• For \( \angle M \): Substitute \( x = 21 \) into \( 6x - 4 \): \( 6(21) - 4 = 126 - 4 = 122 \).
• For \( \angle N \): Substitute \( x = 21 \) into \( x \): \( 21 \).

Answer:

\( m\angle L = 37^\circ \), \( m\angle M = 122^\circ \), \( m\angle N = 21^\circ \)