Question

1. if (mangle knm=(8x - 5)^{circ}) and (mangle mnj=(4x - 19)^{circ}), find the measure of (angle knm).

Explanation:

Step1: Assume linear - pair

Since $\angle KNM$ and $\angle MNJ$ form a linear - pair, their sum is $180^{\circ}$. So, $(8x - 5)+(4x - 19)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $8x+4x-5 - 19 = 180$, which simplifies to $12x-24 = 180$.

Step3: Isolate the variable term

Add 24 to both sides of the equation: $12x-24 + 24=180 + 24$, resulting in $12x=204$.

Step4: Solve for $x$

Divide both sides by 12: $x=\frac{204}{12}=17$.

Step5: Find the measure of $\angle KNM$

Substitute $x = 17$ into the expression for $\angle KNM$. So, $m\angle KNM=8x - 5=8\times17-5=136 - 5=131^{\circ}$.

Answer:

$131^{\circ}$