Question

Is it possible for triangle JKL to be similar to triangle XYZ Explain.

Answer 1

Yes. For two triangles to be similar all corresponding angles have to have the same angle.
J corresponds to X and they are both 71
K corresponds to Y and they are both 52 because 180-(71+57)= 52
L corresponds to Z and they are both 57 because 180-(71+52) = 57

Hope this helped :)

Answer 2

Answer: Yes it is possible for triangle JKL to be similar to triangle XYZ.

Explanation:

Given: In ΔJKL

m∠J=71° , m∠K=52°

In ΔXYZ

m∠X=71° , m∠Z=57°

Using Angle sum property of triangle in ΔJKL, we have

m∠J+m∠K+m∠L=180°

⇒71°+52°+m∠L=180°

⇒m∠L=180°-123°

⇒m∠L=57 °

Now in ΔJKL and ΔXYZ , we have

m∠J=m∠X=71°

and m∠L= m∠Z=57°

Therefore , By AA-similarity criteria , we have

ΔJKL≈ΔXYZ

Hence, Yes it is possible for triangle JKL to be similar to triangle XYZ.