Question

one sided of a 7 sided polygon is 102 degree and all other angles are equal find the equal angles​

Answer 1

Step-by-step-explanation

Given

• One angle of polygon is 102°.
• This Polygon have 7 sides.
• All Other angles are Equal.

To Find

• Equal angles of polygon

Solution

• To Find the all angles of the polygon first we need to find the sum of all interior angles of given polygon.

We use formula

• S = (n-2)×180°

Where,

• S = Sum of interior angles
• n = Number of sides

Putting the value in formula

$\\ \small \sf~~\implies ~~~S = (7-2)×180°$

$\small \sf~~\implies ~~~S =5×180°$

$\small \sf~~\implies ~~~S =900°$

$\small\textsf{Sum of all interior angles of polygon is 900°}$

• it is given that all angles are Equal in polygon and one other angle of the same polygon is 102°. So the sum of all angles of the polygon be 102°+ sum of all Equal angles.

let the all Equal angles be x

therefore

$\sf{~~~~\implies~~~~102+x+x+x+x+x+x =900\degree}$

$\sf{~~~~\implies~~~~102+6x=900\degree}$

$\sf{~~~~\implies~~~~6x=900 - 102}$

$\sf{~~~~\implies~~~~6x=798}$

$\sf{~~~~\implies~~~~x=133 \degree}$

$\frak{Henceforth \: \: the \: Equal \: \: angles \: \: of \: \: polygon \: \: is \: \: 133°}$

Answer 2

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