Question

A polygon has n sides. Two of its sides are right angle while the remaining each side is 144.find n​

Answer 1

Use the formula that states that the sum of the angles of an n-sided polygon is given by
S=(n−2)180
0
........(1)

Since we are given that the two angles are right angles and each of the remaining angles is 144
0
, therefore, the sum is:

S=90
0
+90
0
+(n−2)144
0
.........(2)

Therefore setting (2) equal to (1) we get

(n−2)180
0
=90
0
+90
0
+(n−2)144
0

⇒(n−2)180
0
−(n−2)144
0
=180
0

⇒(n−2)(180
0
−144
0
)=180
0

⇒(n−2)(36
0
)=180
0

⇒n−2=
36
180
​

⇒n−2=5
⇒n=5+2=7

Hence, the polygon has 7 sides.