Question

Angle ABC is a straight angle. mDBC = 130° and bisects ABD.


What is mEBA?

Answer 1

Step-by-step explanation:

if mDBC = 130 then mEBA= 180-130 = 50

50/2= 25

Answer 2

∠EBA = 25°

Step-by-step 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 :)