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Three interior angles of a polygon are 125,140 and 160. The remain angles are 145 each. Calculate the sum of the interior angles of the polygon

Sagot :

Answer:

1440 degrees.

Step-by-step explanation:

125 + 140 + 160 = 425 degrees.

The remaining angles are each 145.

The exterior angles of all polygons sum to 360 .

So we have exterior angles sum of the 3 given angles

= (180-125) + ( 180-140) + (180-160)

= 55 + 40 + 20 = 115.

So the remaining vale of the sum is 360 - 115

= 245 degrees.

An internal angle of 145 will give an external one of 35 degrees.

245/35 = 7.

So there are 7 145 degree angles in the polygon.

Sum of the interior angles is therefore:

425 + 7*145

= 1440 degrees.

This is a 10 sides polygon ( a decagon).

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