Question

Two of the exterior angle of an n-sided polygon are 25° and 26°, three of its interior angles
are 161º each and the remaining interior angles are 159° each. Find the value of n.​

Answer 1

Given :-

• Two of the exterior angle of an n-sided polygon are 25° and 26°.
• three of its interior angles are 161º each .
• the remaining interior angles are 159° each.

To find :-

• Find the value of n . (Number of sides). ?

Concept used :-

• Sum of all exterior angles of a polygon = 360°.
• Sum of Exterior and interior angles of a polygon = 180° .

Solution :-

Lets find all exterior angles of the Polygon first.

→ 2 Exterior angles given = 25° and 26° .

→ sum = 25 + 26 = 51° .

and,

→ three of its interior angles are = 161º each

So,

→ Each Exterior angle = 180° - 161° = 19° .

→ sum of three Exterior angles = 19*3 = 57° .

Now,

→ Total angles Left = n - (2 + 3) = (n - 5) .

and,

→ the remaining interior angles are = 159° each.

So,

→ Each exterior angles of remaining angles = 180° - 159° = 21° .

→ sum of all (n -5) exterior angles left = 21(n - 5) = (21n - 105°) .

Therefore,

→ Sum of all exterior angles = 360°

→ 51° + 57° + (21n - 105°) = 360°

→ 108° - 105° + 21n = 360°

→ 3° + 21n = 360°

→ 21n = 360° - 3°

→ 21n = 357°

→ n = 17 (Ans.)

Hence, Value of n is 17.