A regular polygon of n sides is such that each interior angle is 120^ exto greater than the exterior angle…

Question

A regular polygon of n sides is such that each interior angle is 120^ exto greater than the exterior angle. Find (i) the value of n; (ii) the sum of all the interior angles.

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Here are the solutions to the questions:

Question 7(a):
A regular polygon of $n$ sides is such that each interior angle is $120^\circ$ greater than the exterior angle. Find:

(i) the value of $n$ ;

(ii) the sum of all the interior angles.

Part (i): The value of $n$

Define interior and exterior angles.
Let the interior angle be $I$ and the exterior angle be $E$ .
We know that the sum of an interior angle and its corresponding exterior angle is $180^\circ$ :
$I + E = 180^\circ$
We are given that the interior angle is $120^\circ$ greater than the exterior angle:
$I = E + 120^\circ$
Solve for the exterior angle $E$ .
Substitute the second equation into the first:
$(E + 120^\circ) + E = 180^\circ$ $2E + 120^\circ = 180^\circ$ $2E = 180^\circ - 120^\circ$ $2E = 60^\circ$ $E = \frac{60^\circ}{2}$ $E = 30^\circ$
Calculate the number of sides $n$ .
For a regular polygon

A regular polygon of n sides is such that each interior angle is 120^ exto greater than the exterior angle. Find (i) the value of n; (ii) the sum of all the interior angles.

Step-by-step solution

Define interior and exterior angles.

Solve for the exterior angle $E$ .

Calculate the number of sides $n$ .

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More Mathematics Questions

A regular polygon of n sides is such that each interior angle is 120^ exto greater than the exterior angle. Find (i) the value of n; (ii) the sum of all the interior angles.

Step-by-step solution

Define interior and exterior angles.

Solve for the exterior angle EEE.

Calculate the number of sides nnn.

Still stuck on this one?

More Mathematics Questions

Solve for the exterior angle $E$ .

Calculate the number of sides $n$ .