Answer:
[tex]m[/tex]∠[tex]EBC=65[/tex]° [tex]15'[/tex] and [tex]AC=20in[/tex]
Step-by-step explanation:
Given:
[tex]AB[/tex]≅[tex]BC[/tex]
[tex]AE=10in\\m\angle FEC=90\\m\angle ABC=130\°30'[/tex]
From the given Data, we can conclude the following:
1. Since two sides of the triangle ABC are congruent, therefore its an isosceles triangle.
2. [tex]m\angle FEC=90[/tex]°. This shows that the line BE is perpendicular to AC. By property of isosceles triangle, the line which passes from the vertex of the largest angle of triangle and cuts the opposite side(base) perpendicularly is the perpendicular bisector of the side and angle bisector of the angle.
∴ [tex]m\angle EBA\ ≅m\angle EBC[/tex] [ Definition of Angle bisector]
[tex]m\angle ABC=130\°30'[/tex]
[tex]m\angle EBC=\frac{m\angle ABC}{2}=\frac{130\°30'}{2}=65\°15'[/tex]
[tex]m\angle EBC=65\°15'[/tex]
∴[tex]AE=EC[/tex] [ Definition of perpendicular bisector]
[tex]AE=EC=10in[/tex]
[tex]AC=AE+EC[/tex]
[tex]AC=10+10=20in[/tex]
[tex]AC=20in[/tex]
