Answer:
∠EBA = 25°
Explanation:
We are given that ∠ABC is a straight angle
This means that ∠ABC = 180°
∠ABC can be rewritten as the summation of ∠DBC and ∠DBA
Therefore:
∠ABC = ∠DBC + ∠DBA
We are given that ∠DBC = 130°
Substitute with the givens to get ∠DBA as follows:
∠ABC = ∠DBC + ∠DBA
180° = 130° + ∠DBA
∠DBA = 180° - 130° = 50°
Now, ∠DBA can be rewritten as the summation of ∠DBE and ∠EBA
We are given that the ray BE bisects ∠DBA
This means that ∠DBE = ∠EBA
Therefore:
∠DBA = ∠DBE + ∠EBA = ∠EBA + ∠EBA = 2∠EBA
We have calculated that ∠DBA = 50°
Therefore:
∠DBA = 2∠EBA
50° = 2∠EBA
∠EBA = 25°
Hope this helps :)
