Answer

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**Hint:**To solve this question we need to apply the concept that the total angle in a straight line equals to $180_{}^\circ$.

**Complete step by step answer:**

Since the total angle in a straight line equals to $180_{}^\circ$.

Now from the diagram,

We can write that the sum of $3x$ and $3x$ is equal to $180_{}^\circ$ and the sum of $\Rightarrow 150_{}^\circ$ and $x$ also equals to $180_{}^\circ$.

Therefore, $3x + 3x = 180_{}^\circ$

$\Rightarrow 6x = 180_{}^\circ$

On dividing the terms we get the value of $x$

So, $x = 30_{}^\circ$

Also, we can write

$\Rightarrow x + 150_{}^\circ = 180_{}^\circ$

By moving $150_{}^\circ$ on the right hand side we get-

$\Rightarrow x = 180_{}^\circ - 150_{}^\circ$

On subtracting the terms we get,

$\Rightarrow x= 30_{}^\circ$

**So it is verified that in both the cases the value of x $ = 30_{}^\circ$ since the angles lie on the same straight line. Thus, the correct option is $D$.**

**Note:**

- In mathematics, an angle whose vertex point has a value of 180 degrees is a straight angle. Essentially, it makes a straight line from the vertex, the sides of which lie in opposite directions. They are often referred to as "flat angles".

- A straight angle is exactly half of the revolution that is $360_{}^\circ$.

- A straight angle inverts the point’s path.

- By adding two right angles, a straight angle can be formed.

- By rotating one ray 180° with respect to another ray, a straight angle is created.

- Real-life examples of a straight angle include see-saw, the inclined plane of the staircase, plane surface, straight stick, etc.

- The positive straight angle, that is, $180_{}^\circ$ is a straight angle determined anti-clockwise.

- A negative straight angle, that is, $ - 180_{}^\circ$ is a straight angle determined clockwise.

- The arms extend in the reverse direction at a straight angle.

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