# How many sides do these regular Polygons have if their interior is 30?

The formula for the sum of the interior angles of a regular polygon is given as:

We do not know the number of sides, or the sum of the interior angles.

Lets call the sum of the angles S.

Solving simultaneously:

We could have ascertained this at the beginning. As the number of sides of a polygon increase, the interior angles get larger.

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If the interior angle of a regular polygon is 30 degrees, you can use the formula for the interior angle of a regular polygon, which is given by ( \text{Interior angle} = \frac{(n-2) \times 180}{n} ), where ( n ) is the number of sides of the polygon.

Given that the interior angle is 30 degrees, we can set up the equation:

( 30 = \frac{(n-2) \times 180}{n} )

Solving this equation for ( n ):

( 30n = (n-2) \times 180 )

( 30n = 180n - 360 )

( 360 = 180n - 30n )

( 360 = 150n )

( n = \frac{360}{150} )

( n = 12/5 )

However, since ( n ) represents the number of sides of a polygon, it must be a whole number. Hence, we need to find a common denominator for ( 12/5 ) which is 60.

( n = \frac{12}{5} \times \frac{12}{12} = \frac{144}{60} )

( n = 2.4 )

But, since the number of sides must be a whole number, we round ( 2.4 ) to the nearest whole number which is ( 2 ).

Therefore, if the interior angle of a regular polygon is 30 degrees, the polygon would have 2 sides.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the sum of the interior angle measures in a 20-gon?
- How do you find the perimeter and area of an isosceles triangle whose base is 6cm, leg is 5cm and height is 4cm?
- The sum of the measures of angle X and angle Yis 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X?
- Does anyone know of a theorem or equation that will determine how many diagonals a polygon has, without having to do a drawing to see how many there are?
- What are the proper units for measuring angles?

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