In a triangle, the two angles are 34 and 85 degrees. In the other triangle, one angle is 61 degrees, and the difference

In a triangle, the two angles are 34 and 85 degrees. In the other triangle, one angle is 61 degrees, and the difference between the other two angles is 51 degrees. Are these triangles similar? Why?

To assert such triangles or not, it is necessary to find one of three similarity signs. Obviously, in this problem the first sign will be searched: in two corners.
In triangle 1, two angles are known, the third angle will be: 180 ° – (34 ° + 85 °) = 61 °.
In the second triangle, there are two unknown angles: 180 ° – 61 ° = 119 °. About the same two angles, it is said that the difference in their values is 51 °.
x + 51 ° + x = 119 °
2x = 68 °
x = 34 °.
The angles in triangle 2 are: 61 °, 34 °, 85 °.
We got the equality of the angles of the two triangles.
Answer: Triangles are similar.



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