Question

four angles of the quadrilateral are in the ratio of 2:3:5:8 find least angle​

Answer 1

Answer:

Check out below for the Answer!

Step-by-step explanation:

Four angles of the quadrilateral are in the ratio = 2:3:5:8

Let the angles be 2x, 3x, 5x and 8x.

[Sum of all angles of quadrilateral = 360°]

2x + 3x + 5x + 8x = 360°

18x = 360°

x = $\frac{360}{18}$ [transposed]

x = 20°

2x = 2×20

    = 40°

3x = 3×20

    = 60°

5x = 5×20

    = 100°

8x = 8×20

    = 160°

The angles of the quadrilateral = 40°, 60°, 100°, 160°

Therefore,

The least angle of the Quadrilateral = 2x = 40°

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Answer 2

Given: Four angles of the quadrilateral are in the ratio of 2:3:5:8.

To find: The least angle.

Let the angles of the Quadrilateral be 2x, 3x, 5x and 8x respectively.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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• Sum of all angles of the Quadrilateral is 360°.

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Therefore,

$:\implies\sf 2x + 3x + 5x + 8x = 360 \\\\\\:\implies\sf 18x = 360 \\\\\\:\implies\sf x = \cancel\dfrac{360}{18} \\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 20}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{Angles\; of \; Quadrilateral\; are\: :}}$⠀

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• First angle, 2x = 2(20) = 40°
• Second angle, 3x = 3(20) = 60°
• Third angle, 5x = 5(20) = 100°
• Fourth angle, 8x = 8(20) = 160°

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$\therefore{\underline{\sf{Hence, \; smallest\; angle \: of~ Quadrilateral~ is~ \bf{40^{\circ} }.}}}$