$\\triangle uvw$ and $\\triangle yxw$ are shown below.\nwhich statement is true?\n$\\triangle uvw$ is…

$\\triangle uvw$ and $\\triangle yxw$ are shown below.\nwhich statement is true?\n$\\triangle uvw$ is similar to $\\triangle yxw$.\n$\\triangle uvw$ is not similar to $\\triangle yxw$.\nthere is not enough information to determine whether the triangles are similar.

$\\triangle uvw$ and $\\triangle yxw$ are shown below.\nwhich statement is true?\n$\\triangle uvw$ is similar to $\\triangle yxw$.\n$\\triangle uvw$ is not similar to $\\triangle yxw$.\nthere is not enough information to determine whether the triangles are similar.

Answer

Explanation:

Step1: Find ∠V in △UVW

Sum of angles in triangle is $180^\circ$. $\angle V = 180^\circ - 75^\circ - 45^\circ = 60^\circ$

Step2: Find ∠Y in △YXW

Sum of angles in triangle is $180^\circ$. $\angle Y = 180^\circ - 60^\circ - 45^\circ = 75^\circ$

Step3: Match corresponding angles

In △UVW: $\angle U=75^\circ$, $\angle V=60^\circ$, $\angle W=45^\circ$ In △YXW: $\angle Y=75^\circ$, $\angle X=60^\circ$, $\angle W=45^\circ$ All corresponding angles are equal.

Answer:

$\triangle UVW$ is similar to $\triangle YXW$.