# In triangle XYZ <X=25 deg., <Y=120 deg., & in triangle LMN  <N=45 deg., <M=120 deg. Are they similar?

pohnpei397 | Certified Educator

No, these triangles can not possibly be similar if the information you have provided here is correct.

In similar triangles, all the corresponding angles must be equal to one another.  Given the information we have here, the angles are not equal in both triangles.  Here's why.

We know that the sum of the angles of a triangle must always equal 180 degrees.  Because we know that, we can figure out what angle Z is in triangle XYZ.  Angle X and Angle Y add up to 145 degrees.  That leaves 35 degrees as the measure of Angle Z.

Given this, triangle XYZ is not similar to triangle LMN because only one pair of angles is congruent.  Triangle XYZ's angles are 120,25,35 while triangle LMN's are 120,45,15.

lynn30k | Certified Educator

Similar triangles have all three angles that have the same measure. We already know that both of your triangles have an angle that measures 120 deg. We also know that the three angles of any triangle always add up to 180 degrees.

For triangle XYZ, we have to figure out what the measure of angle Z is. <X is 25, <Y is 120; the two added together = 145 deg. To find <Z, subtract: 180 -145 = 35 deg. When you do the same thing to triangle LMN, we find the measure of < L is 15 deg. (You figure that out yourself, by the way I did <Z)

Therefore, no, they are not similar. The angles of XYZ are 25, 120, and 35, and LMN are 45, 120, and 15 deg.

neela | Student

They are not similar for following reasons:

2 tringles are similar if  (i) their corresponding sides  bear the same ratio or (ii) the angles of one are equal to the that of the other triangle.

Here,in triangle XYZ,  angle X =25 degree, angle Y = 120 degree. Since the sum of all three angles of a triangle are 180 degrees,and therefore, the remaing angle Z = 180 -(25+120) = 35 degree.

In triangle LMN, angle N = 45. There is no angle 45 degree in triangle XYZ. So this is sufficient to disprove that the triangles XYZ and LMN are similar.