Question

one angle of a 7side polygon is 114 and each of other 6 angle are equal. find the angle ​

Answer 1

Question : -

One out of 7 angle of a heptagon is 114° and the rest of the 6 angles are equal. Find the angle.

Answer : -

Given that,

1 out of 7 angle = 114°

Rest of the 6 angles are equal.

To find,

Rest of the 6 angles = ?

Assumption,

Let x be the unknown equal angles.

As we know,

Sum of all the angles of a heptagon = 900°

∴ ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = 900°

But, ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = x

∴ ∠1 + x + x + x + x + x + x = 900°

114° + 6x = 900°

6x = 900° - 114°

6x = 786

x = $\frac{786}{6}$

x = $\frac{\cancel{786}}{\cancel{6}}$

x = 131

[By substituting the values of x],

x = ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7

∴ ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = 131°

Verification : -

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = 900°

[By angle sum property of a heptagon],

114° + x + x + x + x + x + x = 900°

114° + 131° + 131° + 131° + 131° + 131° + 131° + = 900°

900° = 900°

Hence, verified.

Therefore, the unknown angles are 131°.

Answer 2

Given ,

One of the angle = 114°

Rest of the 6 angles are equal.

Let the six angels be x [Given they are equal]

As we know,

Sum of all the angles of a heptagon = 900°

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = 900°

∴ ∠1 + x + x + x + x + x + x = 900°

114° + 6x = 900°

6x = 900° - 114°

6x = 786

x = 786/6

x = 131

Therefore rest of the six angles = 131°

Verification =>

Given ,

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + ∠7 = 900°

[substitute the values]

114 + 131+131+131+131+131+131 = 900

900 = 900

Hence the above answer is verified .