Question

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

Answer 1

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:

\[
\boxed{82}
\]