Question
Download Solution PDFIn ΔABC, perpendiculars AG, BH and CI meet at O. If ∠B = 44°, ∠C = 66°, find the measure of ∠BOC.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In ΔABC, perpendicular bisectors AG, BH and CI meet at O.
∠B = 44°, ∠C = 66°
Concepts used:
Sum of all three angles of triangle is 180°.
The points where perpendiculars meet is orthocentre.
Angle formed at orthocentre by given side = [180° - (angle opposite to given side)]
Calculation:
According to sum angle property of triangle,
∠A + ∠B + ∠C = 180°
⇒ ∠A + 44° + 66° = 180°
⇒ ∠A = 180° - 110°
⇒ ∠A = 70°
Angle formed at orthocentre by given side = [180° - (angle opposite to given side)]
⇒ ∠BOC = 180° - 70° = 110°
∴ ∠BOC is equal to 110°.
Confusion Points The given point is orthocentre, according to the property of orthocentre,
The angle formed on orthocentre = [180° - (angle opposite to given side)]
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