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Question
In a triangle ABC, if ∠A > ∠B > ∠C and the measures of ∠A, ∠B and ∠C in degrees are integers, then the least possible values of A, B and C are _______ and ______ respectively.
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Solution
It is given that, in ∆ABC, ∠A > ∠B > ∠C and the measures of ∠A, ∠B and ∠C in degrees are integers.
So, the least value of ∠C is 1º and the least value of ∠B is 2º.
In ∆ABC,
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
∴ ∠A + 2° + 1° = 180°
⇒ ∠A = 180° − 3° = 177°
In a triangle ABC, if ∠A > ∠B > ∠C and the measures of ∠A, ∠B and ∠C in degrees are integers, then the least possible values of A, B and C are __177°, 2°__ and __1°_ respectively.
Note: The value of ∠A depends upon the values of ∠B and ∠C. The least value of ∠A would be 61º. But, it that case the values of ∠B or ∠C would not be least.
It is given that, in ∆ABC, ∠A > ∠B > ∠C and the measures of ∠A, ∠B and ∠C in degrees are integers.
So, the least value of ∠C is 1º and the least value of ∠B is 2º.
In ∆ABC,
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
∴ ∠A + 2° + 1° = 180°
⇒ ∠A = 180° − 3° = 177°
In a triangle ABC, if ∠A > ∠B > ∠C and the measures of ∠A, ∠B and ∠C in degrees are integers, then the least possible values of A, B and C are __177°, 2°__ and __1°_ respectively.
Note: The value of ∠A depends upon the values of ∠B and ∠C. The least value of ∠A would be 61º. But, it that case the values of ∠B or ∠C would not be least.
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