If triangle ABC has one angle that measures 40 degrees and other that measures 10 degrees, then we can calculate how much the third angle measures, because we know that the sum of the interior angles of a triangle is always 180 degrees, therefore, the third angle measures:
[tex]40+10+x=180[/tex]Solving for "x"
[tex]\begin{gathered} 50+x=180 \\ x=180-50=130 \end{gathered}[/tex]The third angle measures 130 degrees.
Now, we do the same for triangle DEF, since we know that it has an angle that measures 40 degrees and the other measures 120 degrees, we find the third angle like this.
[tex]40+120+x=180[/tex]Solving for "x"
[tex]\begin{gathered} 160+x=180 \\ x=180-160=20 \end{gathered}[/tex]therefore, the third angle of triangle DEF is 20 degrees. Since the triangles don't have the same angles, they are not congruent. The Statement is not true, the explanation should be:
"The statement is never true. By the triangle sum theorem, the third angle of ABC measures 130 degrees and the third angle of DEF measures 20 degrees. since corresponding angles are not congruent the triangles cannot bne congruent"
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