In △ABC, BD ⟂ AC at D and ∠DBC = 25°. E is a point on BC such that ∠CAE = 80°. What is the measure of ∠AEB?

Correct option is D

Given:

In △ABC, BD ⟂ AC at D

∠DBC = 25°

E lies on BC

∠CAE = 80°

Find ∠AEB.

Formula Used:

Sum of all interior angle of triangle = 180⁰ 

Exterior angle of triangle = sum of two opposite interior angle of triangle

Solution: 

In △BDC

Since BD ⟂ AC, ∠CDB = 90°

∠DBC = 25°

=> ∠BCD = 180 − (90 + 25) = 65°

Now, In △ACE

∠AEB = ∠EAC + ∠ACE = 80 + 65 = 145°