Answer:
[tex]m\angle C=100\°[/tex]
Step-by-step explanation:
The correct question is
If triangle ABC is congruent to triangle DEF, m∠A=50° and m∠E=30°. What is m∠C?
we know that
If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent
so
m∠A≅m∠D
m∠B≅m∠E
m∠C≅m∠F
and
AB≅DE
BC≅EF
AC≅DF
we have
m∠A=50°
m∠E=30°
Remember that
m∠B≅m∠E
so
m∠B=m∠E
m∠B=30°
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the triangle ABC
Find the measure of angle C
[tex]m\angle A+m\angle B+m\angle C=180^o[/tex]
substitute the given values
[tex]50\°+30\°+m\angle C=180^o[/tex]
[tex]80\°+m\angle C=180^o[/tex]
[tex]m\angle C=180^o-80\°[/tex]
[tex]m\angle C=100\°[/tex]
