"Two sides and the angle opposite one of them" doesn't uniquely define a triangle. That is,
there can be two or more triangles with different size, or shape, or area that have the same
two sides and the same angle opposite one of them.
In order to use two sides to define a unique triangle, you also have to give the angle between them.
To solve an oblique triangle (a triangle without a right angle), you can use the Law of Sines or the Law of Cosines, depending on the information given. If you have two angles and one side (AAS or ASA), you can apply the Law of Sines to find the unknown sides. If you have two sides and the included angle (SAS) or all three sides (SSS), the Law of Cosines is appropriate. By using these laws, you can find the remaining sides and angles of the triangle.
None, as far as I can see. Which, given that I cannot see any triangle, is not saying much!
The answer is given opposite.
To show that triangle ABC is congruent to triangle DEF by the Angle-Angle-Side (AAS) criterion, you need to establish that one pair of corresponding sides is congruent in addition to the two pairs of corresponding angles. Specifically, if you have already shown that two angles in triangle ABC are congruent to two angles in triangle DEF, you must also demonstrate that one side of triangle ABC is congruent to the corresponding side in triangle DEF that is opposite to one of the given angles.
It can be an obtuse triangle which includes 2 acute angles and the 3 angles add up to 180 degrees
By using the cosine rule in trigonometry the angles of the triangle can be worked out.
To solve an oblique triangle (a triangle without a right angle), you can use the Law of Sines or the Law of Cosines, depending on the information given. If you have two angles and one side (AAS or ASA), you can apply the Law of Sines to find the unknown sides. If you have two sides and the included angle (SAS) or all three sides (SSS), the Law of Cosines is appropriate. By using these laws, you can find the remaining sides and angles of the triangle.
The sides and angles of a triangle are generally described using a,b,c for the three sides and A for the angle opposite side a, B for the angle opposite side b and C for the angle opposite side c. Then use the Sine Rule provided that one of the given angles is opposite the given side. a/Sin A = b/Sin B = c/Sin C
If two angles and the side opposite one of them in one triangle are equal to one side and two similarly located angles in a second triangle then the two triangles are congruent. (The triangles are exactly the same shape and size as each other).
Using the cosine rule in trigonometry the opposite angles to the given dimensions are 17.9 degrees, 120 degrees and 42.1 degrees respectively.
None, as far as I can see. Which, given that I cannot see any triangle, is not saying much!
Remote interior angles
An obtuse or a scalene triangle would have angles of the given sizes
It is impossible to find a triangle if only angle measures are given (all similar triangles have the same angles).
The answer is given opposite.
To show that triangle ABC is congruent to triangle DEF by the Angle-Angle-Side (AAS) criterion, you need to establish that one pair of corresponding sides is congruent in addition to the two pairs of corresponding angles. Specifically, if you have already shown that two angles in triangle ABC are congruent to two angles in triangle DEF, you must also demonstrate that one side of triangle ABC is congruent to the corresponding side in triangle DEF that is opposite to one of the given angles.
A scalene triangle would have angles of the given sizes.