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# 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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## Text solutionVerified

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 = 12
Smallest angle is :
∠A = 3x
∠A = 3(12°)
∠A = 36°
Hence, the smallest angle measures 36°.
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 Question Text If the angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13, then find the measure of the smallest angle. Updated On Apr 29, 2023 Topic Quadrilaterals Subject Mathematics Class Class 9 Answer Type Text solution:1 Video solution: 2 Upvotes 277 Avg. Video Duration 9 min
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