Question

In a polygon 3 interior angles are 150 each , 2 exterior angles 100 each and remaining exterior angles are 35 each. find the number of sides.

Answer 1

Answer:

7

Step-by-step explanation:

3 interior angles are 150 each, so their exterior angles would be (180-150)=30 degrees

therefore- 3 exterior angles=30+30+30=90 degrees...(i)

2 exterior angles are 100 degrees each, so 100+100=200 degrees....(ii)

Adding (i) and (ii) i.e 90+200

=290 degrees

we know that the sum of exterior angles of any polygon is 360 degrees

so, 360-290=70

and as it was given in question that the remaining exterior angles are 35 degree each, so 2 such angles would be required so as to attain 70 degree... which will make the sum of exterior angles 360.

so, total no. of sides= 3+2+2

= 7