Question

using the image provided, find m∠lmd.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle $\triangle LCM$ is $180^{\circ}$. So, $(6n - 14)+(4n - 5)+ \angle LMC=180$. Also, $\angle LMC+(8n - 5)=180$ (linear - pair of angles). Then, $\angle LMC = 180-(8n - 5)=185 - 8n$.
Substitute $\angle LMC$ into the triangle's angle - sum equation:
$(6n - 14)+(4n - 5)+(185 - 8n)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(6n+4n - 8n)+(-14 - 5 + 185)=180$.
$2n+166 = 180$.

Step3: Solve for $n$

Subtract 166 from both sides: $2n=180 - 166=14$.
Divide both sides by 2: $n = 7$.

Step4: Find $m\angle LMD$

Substitute $n = 7$ into the expression for $\angle LMD=(8n - 5)$.
$m\angle LMD=8\times7 - 5=56 - 5=51^{\circ}$.

Answer:

$51^{\circ}$