In triangle ABC, BD ⊥ AC. E is a point on BC such that ∠BEA = x°. If ∠EAC = 38° and ∠EBD = 40°, then the value of x is:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 88°
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Understanding |
Application |
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Given ∠EAC = 38, ∠EBD = 40 and ∠BEA = x Since BD is perpendicular to AC, ∠BDA = 90
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In the figure: ∠BOA is the external angle of triangle BOE Hence, ∠BOA = ∠OBE + ∠OEB ⇒ ∠BOA = (40 + x) And ∠AOD = 180 – (40 + x) ⇒ ∠AOD = (140 – x) Now in triangle AOD: 38 + (140 – x) + 90 = 180 ⇒ 268 – x = 180 ⇒ x = 268 – 180 = 88° |
