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I think angle abc is 80° and angle fec is 90°

Explanation:

Since angle abe is 40° just double it to get abc

And fec is just a 90° angle

The median of the isosceles triangle ABC bisects the side AC, forming two

congruent triangles ΔBAE and ΔBEC.

  • m∠ABC = 81°
  • m∠FEC = 90°

Reasons:

Given parameters are;

In ΔABC

AB is congruent to BC; AB ≅ BC

A median of ΔABC = BE

m∠ABE = 40°30'

Required:

m∠ABC

Solution:

AB ≅ BC

∴ AB = BC,  ∴ ΔABC is an isosceles triangle

∠BAE = ∠BCE base angles of an isosceles triangle ΔABC

Line BE bisects AC; definition of median line

AE = EC definition of bisected line

ΔBAE ≅ ΔBEC by Side-Angle-Side rule of congruency

∠ABE = ∠CBE by Congruent Parts of Congruent Triangles are Congruent, CPCTC

∠ABC = ∠ABE + ∠CBE by angle addition postulate

∴ ∠ABC = ∠ABE + ∠ABE = 2× ∠ABE by substitution property

m∠ABC = 2 × 40°30' = 81°

  • m∠ABC = 81°

∠FEC = ∠BEA by vertical angle theorem

∠BEA = ∠BEC by CPCTC

∠BEA + ∠BEC = 180° by linear pair angles

∴ 2 × ∠BEA = 180°

[tex]\angle BEA = \dfrac{180^{\circ}}{2} = 90^{\circ}[/tex]

m∠FEC = m∠BEA = 90°

  • m∠FEC = 90°

Learn more here:

https://brainly.com/question/21495359

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