Question

in triangle uvw, the measure of ∠wuv is 110° and the measure of ∠uvw is 38°. in triangle xyz, the measure of ∠zxy is 110° and the measure of ∠yzx is 32°. determine how triangles uvw and xyz can be shown to be similar. a. since ∠wuv ≅ ∠zxy and uv = yz, the triangles are similar by angle - side. b. since ∠wuv ≅ ∠zxy and uv = xz, the triangles are similar by angle - side. c. since ∠wuv ≅ ∠zxy and ∠uvw ≅ ∠yzx, the triangles are similar by angle - angle. d. since ∠wuv ≅ ∠zxy and ∠uvw ≅ ∠xyz, the triangles are similar by angle - angle.

Explanation:

Step1: Identify given angles

In △UVW: ∠WUV = 110°, ∠UVW = 38°.
In △XYZ: ∠ZXY = 110°, ∠YZX = 32°.
Check equal angles: ∠WUV ≅ ∠ZXY (both 110°).

Step2: Calculate third angles

△UVW third angle: ∠WVU = 180° - 110° - 38° = 32°.
△XYZ third angle: ∠XYZ = 180° - 110° - 32° = 38°.
Now: ∠UVW (38°) ≅ ∠XYZ (38°), ∠WVU (32°) ≅ ∠YZX (32°).

Step3: Apply AA similarity

Two pairs of equal angles (∠WUV≅∠ZXY, ∠UVW≅∠XYZ or ∠WVU≅∠YZX) satisfy AA similarity.
Option C states two equal angle pairs and AA, which is correct.

Answer:

C. Since ∠WUV ≅ ∠ZXY and ∠UVW ≅ ∠YZX, the triangles are similar by angle-angle.