Question

3 of the exterior angles of an n- sided polygon are 50 each, 2 of its interior angles are 127 and 135, and the remaining interior angles are 173 each. find the value of n.

Answer 1

Answer:

Three of the exterior angles of an n sided polygon are 50 each, two of its interior angles are 127 and 135 and the remaining exterior angles are 173 each. ... These are of the 112/(180–173) = 112/7 = 16 angles. Hence n = 5+16 or 21.

Step-by-step explanation:

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Answer 2

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number of sides = n

3 exterior angles are = 50° each

2 interior angles are = 127° and 135°

remaining interior angles = 173° each.

let no. of remaining interior angles be = x

then thier sum = 173x

sum of all interior angles = 173x + 127 + 135

= 173x + 262

Sum of all interior angles of a polygon with n sides = (n-2) X 180

so,

(n-2) X 180 = 173x + 262

$n = \frac{173x + 622}{180}$ - i

sum of 3 exterior angles = 50 X 3 = 150°

On dividing equation 1 with 2

we get

n = 21 sides.