In the figure, the measures of some angles in degrees are indicated as functions of $x$. What is the value of $x$?
(a) $6^{\circ}$

(b) $12^{\circ}$

(c) $18^{\circ}$

(d) $20^{\circ}$

(e) $24^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-009.jpg?height=406&width=680&top_left_y=268&top_left_x=768)
The correct option is (c).

We complete the figure by marking the angles $\alpha$ and $\beta$, remembering that vertically opposite angles are equal. Recall that the sum of the interior angles of a triangle is $180^{\circ}$. Looking at the leftmost triangle, we see that

$$
3 x+4 x+\alpha=180^{\circ} \text {. }
$$

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-045.jpg?height=459&width=762&top_left_y=1935&top_left_x=1047)

It follows that $\alpha=180^{\circ}-7 x$. Considering the middle triangle, we have

$$
\left(180^{\circ}-7 x\right)+5 x+\beta=180^{\circ}
$$

We conclude that $\beta=2 x$. Finally, from the rightmost triangle, we have $\beta+2 x+6 x=180^{\circ}$, that is, $2 x+2 x+6 x=180^{\circ}$. Thus, $x=18^{\circ}$.