Question

find the values of x and y. x = 13 y =

Explanation:

Step1: Find the measure of angle $KNL$

Since the measure of angle $MNL$ is $84^{\circ}$ and the measure of angle $MNL$ is composed of angle $KNL$ and the $43^{\circ}$ angle, we can find angle $KNL$ by subtraction. So, $\angle KNL=84^{\circ}- 43^{\circ}=41^{\circ}$.

Step2: Solve for $x$

We are given that $\angle KNL=(4x - 11)^{\circ}$, and we found that $\angle KNL = 41^{\circ}$. So we set up the equation $4x-11 = 41$.
Adding 11 to both sides gives $4x=41 + 11=52$.
Dividing both sides by 4 gives $x=\frac{52}{4}=13$.

Step3: Solve for $y$

We know that angle $JNK$ and angle $KNL$ are complementary (since $\angle JNL = 90^{\circ}$). So $\angle JNK=90^{\circ}-\angle KNL$. Since $\angle KNL = 41^{\circ}$, then $\angle JNK = 90 - 41=49^{\circ}$.
We are given that $\angle JNK=(7y)^{\circ}$. So we set up the equation $7y=49$.
Dividing both sides by 7 gives $y=\frac{49}{7}=7$.

Answer:

$y = 7$