Answer:
m∠ABC = 81°
m∠FEC = 90°
Explanation:
A median of a triangle is a line segment from the vertex to the mid-point of the side opposite that vertex.
If AB ≅ BC then triangle ABC is an isosceles triangle.
Therefore, if BE is the median of triangle ABC, then m∠ABE ≅ m∠CBE.
Therefore, the measure of ∠ABC is twice the measure of ∠ABE.
First, convert the given measure of ∠ABE into decimal degrees.
Therefore, m∠ABE = 40.5°.
If m∠ABC is twice the measure of ∠ABE:
As triangle ABC is an isosceles triangle where AB≅BC, the median BE is perpendicular to AC. Therefore, m∠FEC = 90°.