J's answer to :-)'s Secondary 3 E Maths Singapore question.
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a)
Recall the property that angle at centre = 2 × angle at circumference
In this question, your angle at circumference is ∠ ABC and angle at centre is reflex ∠ AOC (The relevant segment here is major segment AC)
Reflex ∠ AOC = 360° - ∠ AOC = 143° = 217° (sum of angles at a point)
∠ ABC = Reflex ∠ AOC ÷ 2 = 217° ÷ 2 = 108.5°
b)
∠OAB = 360° - ∠ ABC - ∠ AOC - ∠ OCB (sum of angles in a quadrilateral = 360°)
= 360° - 108.5° - 143° - 62°
= 46.5°
Recall the property that angle at centre = 2 × angle at circumference
In this question, your angle at circumference is ∠ ABC and angle at centre is reflex ∠ AOC (The relevant segment here is major segment AC)
Reflex ∠ AOC = 360° - ∠ AOC = 143° = 217° (sum of angles at a point)
∠ ABC = Reflex ∠ AOC ÷ 2 = 217° ÷ 2 = 108.5°
b)
∠OAB = 360° - ∠ ABC - ∠ AOC - ∠ OCB (sum of angles in a quadrilateral = 360°)
= 360° - 108.5° - 143° - 62°
= 46.5°
Date Posted:
3 years ago
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