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Question
An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are
Options
48°, 60°, 72°
50°, 60°, 70°
52°, 56°, 72°
42°, 60°, 76°
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Solution
In the given ΔABC, an exterior angle ∠ADC = 108° and its interior opposite angles are in the ratio 4:5.
Let us take,
∠A = 4x
∠B = 5x
Now using the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”
We get,
∠A + ∠B = 108°
4x + 5x = 108°
9x = 108°
`x = (108°)/ 9`
x = 12
Thus,
∠A = 4x = 4(12°) = 48°
∠B = 5x = 5(12°) = 60°
Also, using angle sum property in ΔABC
∠A + ∠B + ∠C = 180°
48° + 60° + ∠C = 180°
108° + ∠C = 180°
∠C = 180° - 108°
∠C = 72°
Thus,
∠A = 48°
∠B = 60°
∠C = 72°
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