Answer:
The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.
Step-by-step explanation:
According to exterior angle theorem: It a triangle
Exterior angle = Sum of opposite interior angles
In triangle BED,
[tex]\angle AEF=\angle B+\angle D[/tex]
[tex]82=\angle B+28[/tex]
[tex]82-28=\angle B[/tex]
[tex]54=\angle B[/tex]
The measure of angle B is 54°.
In triangle ABC,
[tex]\angle ACD=\angle A+\angle B[/tex]
[tex]105=\angle A+54[/tex]
[tex]105-54=\angle A[/tex]
[tex]51=\angle A[/tex]
The measure of angle A is 51°.
In triangle AEF,
Using angle sum property,
[tex]\angle A+\angle E+\angle AFE=180[/tex]
[tex]51+82+\angle AFE=180[/tex]
[tex]133+\angle AFE=180[/tex]
[tex]\angle AFE=180-133[/tex]
[tex]\angle AFE=47[/tex]
Therefore the measure of angle AFE is 47°.