Math / Geometry

QuestionEn la siguiente figura, $m \angle M K J=137^{\circ}$ . (a) Escribir una ecuación para hallar x. Asegurarse de utilizar un signo de "=" en su respuesta.
Ecuación: $\square$ (b) Resolver para $x$ . $\square$ $x=$

Studdy Solution

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 $x$ :
$6x = 360 - 208$
$6x = 152$

STEP 6

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:
$x = \frac{76}{3}$

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QuestionEn la siguiente figura, $m \angle M K J=137^{\circ}$ . (a) Escribir una ecuación para hallar x. Asegurarse de utilizar un signo de "=" en su respuesta.
Ecuación: $\square$ (b) Resolver para $x$ . $\square$ $x=$

Studdy Solution

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 $x$ :
$6x = 360 - 208$
$6x = 152$

STEP 6

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:
$x = \frac{76}{3}$

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QuestionEn la siguiente figura, m∠MKJ=137∘m \angle M K J=137^{\circ}m∠MKJ=137∘. (a) Escribir una ecuación para hallar x. Asegurarse de utilizar un signo de "=" en su respuesta.Ecuación: □\square□ (b) Resolver para xxx. □\square□ x=x=x=

Studdy Solution

STEP 1

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

STEP 2

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

STEP 3

STEP 4

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

STEP 5

Subtract 208 208 208 from both sides to isolate the term with x x x:6x=360−208 6x = 360 - 208 6x=360−2086x=152 6x = 152 6x=152

STEP 6

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QuestionEn la siguiente figura, $m \angle M K J=137^{\circ}$ . (a) Escribir una ecuación para hallar x. Asegurarse de utilizar un signo de "=" en su respuesta.
Ecuación: $\square$ (b) Resolver para $x$ . $\square$ $x=$

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 $\angle LKM = (6x)^\circ$ .

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

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

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