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Question
If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle.
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Solution
We have, ∠A : ∠B : ∠C :∠D = 3 : 5 : 9 : 13 .
So, let ∠A = 3x,
∠B = 5x,
∠C = 9x
and ∠D = 13x
By angle sum property of a quadrilateral, we get:
∠A + ∠B + ∠C + ∠D = 360
3x + 5x + 9x + 13x = 360
30x = 360
`x =(360)/(30) `
x = 12
Smallest angle is :
∠A = 3x
∠A = 3(12°)
∠A = 36°
Hence, the smallest angle measures 36°.
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