Answer:
The measure of angle B is 54°. The measure of angle A is 51°. The measure of angle AFE is 47°.
Explanation:
According to exterior angle theorem: It a triangle
Exterior angle = Sum of opposite interior angles
In triangle BED,
![\angle AEF=\angle B+\angle D](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ko3vlk6uc8r6mit2g0lnr9l6utxvs5fht4.png)
![82=\angle B+28](https://img.qammunity.org/2020/formulas/mathematics/middle-school/e6uoxav1ugfj0fearlkksykeclup2g8a5l.png)
![82-28=\angle B](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lqdbr46v9o9pdfqce5scxml4hcg89pxq30.png)
![54=\angle B](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jv8epda5yx6gnnh4yw6iwcvmz6gyx34lln.png)
The measure of angle B is 54°.
In triangle ABC,
![\angle ACD=\angle A+\angle B](https://img.qammunity.org/2020/formulas/mathematics/middle-school/wede5caeh960wiqvykerdgkxfmo2dytz68.png)
![105=\angle A+54](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yti9tm9m6ve8r9lx38p3tepf34abmynh8z.png)
![105-54=\angle A](https://img.qammunity.org/2020/formulas/mathematics/middle-school/iwn08o24kutpubsys3ykv6dk3jneqgnohu.png)
![51=\angle A](https://img.qammunity.org/2020/formulas/mathematics/middle-school/l80fikqyrmyzdstbvpinbsoakq6xs5zw5k.png)
The measure of angle A is 51°.
In triangle AEF,
Using angle sum property,
![\angle A+\angle E+\angle AFE=180](https://img.qammunity.org/2020/formulas/mathematics/middle-school/73qrzvo4rtgya33a0vz1t3a78cz3v7anys.png)
![51+82+\angle AFE=180](https://img.qammunity.org/2020/formulas/mathematics/middle-school/797rpvk9l4wwpwqtshz8rmqogl06uxdwve.png)
![133+\angle AFE=180](https://img.qammunity.org/2020/formulas/mathematics/middle-school/wl8i799bomjflmndft6m3feckm65ct1pm7.png)
![\angle AFE=180-133](https://img.qammunity.org/2020/formulas/mathematics/middle-school/l6yfr0wj3xhftt7yri2suddp86u1cge7jp.png)
![\angle AFE=47](https://img.qammunity.org/2020/formulas/mathematics/middle-school/r1dx45co4ivv2dza2fo7nwn5qyyz93rrzp.png)
Therefore the measure of angle AFE is 47°.