In △ABC, BD ⟂ AC at D and ∠DBC = 22°. E is a point on BC such that ∠CAE = 36°. What is the measure of ∠AEB?

Question

Question

This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 3)

Answer 1

Given:

In Δ ABC, BD ⊥ AC at D and ∠DBC = 22º. E is a point on BC such that ∠CAE = 36º.

Formula Used:

Sum of angles in a Δ = 180º

Calculation:

In Δ BDC, since BD ⊥ AC:

∠BDC = 90º

We have, ∠DBC = 22º

Then, ∠BDC + ∠DCB + ∠DBC = 180º

⇒ 90º + ∠DCB + 22º = 180º

⇒ ∠DCB = 180º - 112º

⇒ ∠DCB = 68º

In Δ AEC, ∠CAE = 36º

Then, ∠AEB = ∠CAE + ∠DCB

⇒ ∠AEB = 36º + 68º

⇒ ∠AEB = 104º

Correct option is 104° .