In the given figure, $T U=S V$. What is the measure of the angle $S \widehat{V} U$, in degrees?
(a) 30
(d) 65
(b) 50
(e) 70
(c) 55

![](https://cdn.mathpix.com/cropped/2024_05_01_280b19a87fa67143351eg-013.jpg?height=329&width=600&top_left_y=1977&top_left_x=1276)
The correct option is (d).

Remember that the sum of the interior angles of a triangle is $180^{\circ}$. From triangle $\triangle S T U$, we have that $T \widehat{S} U=180^{\circ}-\left(75^{\circ}+30^{\circ}\right)=75^{\circ}$. Therefore, this triangle is isosceles (by having two equal angles) and, thus, $T U=S U$. Since $T U=S V$, it follows that $S U=S V$. Hence, triangle $\triangle S U V$ is also isosceles, and therefore,

$$
S \widehat{V} U=\frac{1}{2}\left(180^{\circ}-50^{\circ}\right)=65^{\circ}
$$