Find the measurement indicted in each parallelogram

Find m<J
top left corner K
bottom left corner J
top right corner L
bottom right corner M
inner top left corner 10+11x
inner bottom left corner 10x+2
what is the answer
50
91
82
150

1 answer

To solve for the measurement of angle \( J \) in the parallelogram, we will use the properties of parallelograms.

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (their measures add up to 180 degrees). From the details you've provided, we have the following angles:

  • \( m \angle K = 10 + 11x \)
  • \( m \angle J = 10x + 2 \)

Since angles \( K \) and \( J \) are consecutive angles in the parallelogram, they are supplementary:

\[ m \angle K + m \angle J = 180^\circ \]

Substituting the expressions for \( m \angle K \) and \( m \angle J \):

\[ (10 + 11x) + (10x + 2) = 180 \]

Combining like terms:

\[ 10 + 11x + 10x + 2 = 180 \] \[ 21x + 12 = 180 \]

Now, subtract 12 from both sides:

\[ 21x = 180 - 12 \] \[ 21x = 168 \]

Next, divide both sides by 21 to solve for \( x \):

\[ x = \frac{168}{21} = 8 \]

Now that we have \( x \), we can substitute back to find \( m \angle J \):

\[ m \angle J = 10x + 2 = 10(8) + 2 = 80 + 2 = 82 \]

Thus, the measurement of angle \( J \) is:

\[ \boxed{82} \]