Question

In a pentagon 2 angles are 40 degree and 60 degree and the resr are in the ratio 1:3:7.Find the biggest angle of the pentagon

Answer 1

Hey Buddy

Here is the answer

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We know, Pentagon has 5 sides

So total sum of angles should be

(n-2)×180 = sum of angles

here, n = 5

So

sum = (5-2)×180°

sum = 3×180°

Sum = 540°

Now , Also

40 + 60 + x + 3x + 7x = 540°

100 + 11x = 540

11x = 440

x = 40°

So,

7x => 7 × 40 = 280°

hence 280° is the biggest angle

Hope helped

:)

Answer 2

Answer:

Let {x} be the common ratio

Then, we have

X : 3x :7x

And other two angle = 40, 60

$we \: know \: that \: sum \: of \: all \: \\ angle \: of \: a \: pentao \\ gone \: is \: {180}^{o}$

${40}^{o} + {60}^{o} + {x}^{o} + {3x}^{o} + {7x}^{o} = 540 \\ 11x + 100 = 540 \\ 11x = 540 - 100 \\ 11x = 440 \\ (x = 40)$

$so \: we \: have \: \\ x = {40}^{o} \\ 3x = {120}^{o} \\ {7x}^{} = {280}^{o } \\ the \: biggest \: angle \: is \: 280$

Hope it helps you

Thanks