We are given a diagram where line $MN$ is parallel to line $PQ$. We are given that $\angle MNP = 2x$ and $\angle NPQ = (3x - 50)$. We need to find the value of $\angle NPQ$.

1. Problem Description

We are given a diagram where line $MN$ is parallel to line $PQ$. We are given that $\angle MNP = 2x$ and $\angle NPQ = (3x - 50)$. We need to find the value of $\angle NPQ$.

2. Solution Steps

Since $MN$ is parallel to $PQ$, the angles $\angle MNP$ and $\angle NPQ$ are supplementary angles. This means that their sum is 180 degrees.

So we have:

$\angle MNP + \angle NPQ = 180$

$2x + (3x - 50) = 180$

$5x - 50 = 180$

$5x = 180 + 50$

$5x = 230$

$x = \frac{230}{5}$

$x = 46$

Now we need to find the value of $\angle NPQ$.

$\angle NPQ = 3x - 50$

$\angle NPQ = 3(46) - 50$

$\angle NPQ = 138 - 50$

$\angle NPQ = 88$

However, the given options do not include $88^\circ$. Let us check the calculation of $x$:

$2x + 3x - 50 = 180$

$5x = 230$

$x = 46$

Now we substitute x=46 into $3x - 50$:

$3(46) - 50 = 138 - 50 = 88$.

Let's reconsider the problem. The angles $\angle MNP$ and $\angle NPQ$ are interior angles on the same side of the transversal $NP$. Because the lines $MN$ and $PQ$ are parallel, the angles are supplementary. Thus, $2x + (3x - 50) = 180$, which leads to $5x - 50 = 180$, and $5x = 230$, giving $x = 46$. Then, $\angle NPQ = 3x - 50 = 3(46) - 50 = 138 - 50 = 88$. None of the choices is $88^\circ$. Let's carefully re-examine the diagram and problem statement.

There must be a mistake in the image or choices. Let's assume the correct answer is

1

0

0. In that case:

$3x - 50 = 100$

$3x = 150$

$x = 50$

$2x = 100$

So $2x + 3x - 50 = 180$

$100 + 100 = 200 \neq 180$.

Since none of the options seems right, we have to pick the best option. We obtained 88 degrees.

A. 200

B. 150

C. 120

D. 100

100 is the closest option.

3. Final Answer

D. 100°