Answer:
Yes, the two similar triangles because there are two pairs of congruent corresponding angles
Step-by-step explanation:
from the give figure:
In ΔUTV
\(\angle U = 80^{\circ}\)
\(\angle V= 55^{\circ}\)
By angle sum property of triangle;
\(\angle U + \angle V + \angle T = 180^{\circ}\)
Substitute the given values;
\(80^{\circ}+ 55^{\circ} + \angle T = 180^{\circ}\)
\(135^{\circ} + \angle T = 180^{\circ}\)
⇒\(\angle T = 180^{\circ}- 135^{\circ} = 45^{\circ}\)
Now, In ΔUTV and ΔYXW
\(\angle V = \angle W = 55^{\circ}\)
\(\angle T = \angle X = 45^{\circ}\)
AA similarity postulate states that the two triangles are similar if they have two corresponding angles that are congruent or equal in measure.
so, by AA similarity;
\(\triangle UVT \sim \triangle YXW\)
