Question

four angle of a quadrilateral are in the ratio 4:8:16:32 the greatest angle is __________​

Answer 1

Answer:

192°

Step-by-step explanation:

sum of angles in a quadrilateral is 360 degree

let the common factors of the ratio be x

so the angles are

4x

8x

16x

32x

4x+8x+16x+32x=360°

60x=360°

x=6°

largest is obviously 32x=32×6=192°

so answer is 192°

hope it helps

pls mark as brainliest

Answer 2

${\large{\bf{\red{\underline{Given :}}}}}$

• Four angle of a quadrilateral are in the ratio 4:8:16:32.

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${\large{\bf{\blue{\underline{To Find :}}}}}$

• Find the measure of largest angle.

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${\large{\bf{\orange{\underline{Solution :}}}}}$

Remember that :

Sum of all angles of quadrilateral = 360°

Let the ratios be x :

${\sf{\purple{4x}}}$

${\sf{\purple{8x}}}$

${\sf{\purple{16x}}}$

${\sf{\purple{32x}}}$

Now,

${\sf{\purple{4x + 8x + 16x + 32x = 360°}}}$

${\sf{\purple{60x = 360°}}}$

${\sf{\purple{X = {\cancel\frac{360}{60} }}}}$

${\red{\boxed{\bf{X = 6}}}}$

Than,

${\red{\mapsto{\bf{Angle \: 1 = 4x = 4 \times 6 = 24°}}}}$

${\red{\mapsto{\bf{Angle \: 2 = 8x = 8 \times 6 = 48°}}}}$

${\red{\mapsto{\bf{Angle \: 3 = 16x = 16 \times 6 = 96°}}}}$

$</p><p>{\red{\mapsto{\bf{Angle \: 4 = 32x = 32 \times 6 = 192°}}}}$

For varification :

24° + 48° + 96° + 192° = 360°

$\: \: \: \: \: \: \: \: \: \: \: \: {\red{\underbrace{\blue{\bf{Hence ,Verified}}}}}$

So,

${\sf{\green{Th e \: largest \: angle \: is \: 192°.}}}$

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