Question

Three angles of a 8 sided polygon are 1450

and the remaining 5 angles are equal. Find the magnitude

of each of the equal angles​

Answer 1

Question:

Three angles of a 8 sided polygon are 145°

and the remaining 5 angles are equal. Find the magnitude of each of the equal angles.

Answer :

Info Req. :—»

Sum of angles of a polygon with n sides is (n-2)180

Given :—»

8 sided polygon

Magnitude of 3 angles

Equality of other angles {all other[5 angles] are equal to each other}

To find :—»

Magnitude of every other angle {which is same}

Solution :—»

Sum of angles of a 8 sided polygon =

$\longrightarrow$(n-2)×180

$\longrightarrow$(8-2)×180

$\longrightarrow$6×180

$\longrightarrow$1080°

Sum of three equal angles =

$\longrightarrow$145×3

$\longrightarrow$435°

Let Every other Angle be θ

So, the sum of those 5 equal angles =

$\longrightarrow$5×θ

$\longrightarrow$5θ

Now, To find θ We can subtract the sum of the three equal angles from the sum of all angles

1080°-435°=5θ

5θ = 645°

θ = 645/5 = 129°

129° IS THE MAGNITUDE OF EACH OF THE 5 EQUAL ANGLES