Question
Download Solution PDFIn Δ ABC, BD ⊥ AC at D and ∠DBC = 54º. E is a point on BC such that ∠CAE= 34º. What is the measure of ∠AEB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In Δ ABC, BD ⊥ AC at D and ∠DBC = 54º. E is a point on BC such that ∠CAE = 34º.
Formula Used:
Sum of angles in a Δ = 180º
Calculation:
In Δ BDC, since BD ⊥ AC:
∠BDC = 90º
We have, ∠DBC = 54º
Then, ∠BDC + ∠DCB + ∠DBC = 180º
⇒ 90º + ∠DCB + 54º = 180º
⇒ ∠DCB = 180º - 144º
⇒ ∠DCB = 36º
In Δ AEC, ∠CAE = 34º
Then, ∠AEB = ∠CAE + ∠DCB
⇒ ∠AEB = 34º + 36º
⇒ ∠AEB = 70º
Correct option is 70° .
Last updated on Jun 30, 2025
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