Four students were asked to label angles in pairs of triangles. their drawings are shown below.

The student who labeled the triangle correct such that:

                 ΔABC ~ ΔXYZ

               is:  Kai

For ΔABC ~ ΔXYZ

we must have that:

      m∠A=m∠X

      m∠B=m∠Y

and  m∠C=m∠Z

From the labeling that is done by Tatyanna we see that :

m∠C≠m∠Z

Hence, Tatyana labeled the triangles incorrect.

Similarly the labeling done by Simon is also incorrect.

Since according to him m∠A≠m∠X

( Since, by looking at the triangle XYZ we are given two angle measure with the help of which the third angle measure could be calculated by using the property that the sum of all the angles of a triangle is: 180°

i.e.  ∠X+∠Y+∠Z=180

i.e. ∠X+63.2+58.4=180

i.e. ∠X=180°-(63.2°+58.4°)

i.e. ∠X=180°-(121.6°)

i.e.  ∠X=58.4° )

Hence, Simon labeled the triangle incorrect.

Anders--

( In ΔABC we have:

∠A+∠B+∠C=180°

⇒ 59.8°+60.6°+∠C=180°

⇒ ∠C=59.6°  )

Here as m∠C≠m∠Z

Hence, Anders labeled the triangle incorrect.

Kai--

(   In ΔABC we have:

∠A+∠B+∠C=180°

⇒  ∠A+60.9°+57.7°=180°

⇒ ∠A=61.4°

Similarly in ΔXYZ we get:

∠Y=60.9°  )

Hence, Kai labeled the triangle correct.

Since, m∠A=m∠X

          m∠B=m∠Y

          m∠C=m∠Z