Math Snap

STEP 1

1. The sum of angles around a point is $360^\circ$.
2. We have three angles: $\angle MKJ = 137^\circ$, $\angle JKL = 71^\circ$, and $\angle LKM = (6x)^\circ$.

STEP 2

1. Write an equation for the sum of the angles.
2. Solve for $x$.

STEP 3

We know the sum of angles around point $K$ is $360^\circ$. Therefore, we can write the equation:
$$\angle MKJ + \angle JKL + \angle LKM = 360^\circ$$ Substitute the given values into the equation:
$$137^\circ + 71^\circ + (6x)^\circ = 360^\circ$$ Ecuación: $137 + 71 + 6x = 360$

STEP 4

Now, solve the equation for $x$.
First, simplify the left side of the equation:
$$137 + 71 = 208$$ So the equation becomes:
$$208 + 6x = 360$$

STEP 5

Subtract $208$ from both sides to isolate the term with $x$:
$$6x = 360 - 208$$ $$6x = 152$$

Divide both sides by $6$ to solve for $x$:
$$x = \frac{152}{6}$$ $$x = 25.3333\ldots$$ Since $x$ is typically an integer in these types of problems, we can express it as a fraction:
$$x = \frac{76}{3}$$ The solution for $x$ is:
$$x = \frac{76}{3}$$