Question

please help me with this question ​

Answer 1

ANSWER

(a) ∠BOD = 71°

(b) ∠AEO = 71°

We cannot deduce AE = AB, but AE = AO is proved below.

∠A = ∠D = 90

∠C = 52

So, ∠B = 180-90-52 = 180-142 = 38

BE is bisector of ∠B, hence it means that ∠B is divided in two equal parts and where BE intersects AC is the median,

so AE = CE

and ∠DBO = ∠ABO = 38/2 = 19

In triangle, △BOD

∠BOD = 180-90-19 = 180-109 = 71

As line BE and AD are intersecting at O,

Hence, ∠BOD = ∠AOE = 71 (congruent angles as they are vertical angles of two intersecting line)

in △ABE

∠AEB (or ∠AEO) = 180 - 90 - 19 = 180 - 109 = 71

in △AOE

∠AEO = ∠AOE = 71

△AOE is isosceles triangle

Hence, AE = AO