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Calculate number of sides of a regular polygon has if an interior angle is five times the size of an exterior angle?
Suppose the interior angle is x degrees.
Then the exterior angle is 180 - x degrees.
x = 5*(180-x) = 900 - 5x
So 6x = 900 so that x = 150 degrees.
So exterior angle = 30 degrees.
If the polygon has n sides (and n angles) the sum of its exterior angles is 30*n
But the exterior angles of a polygon add to 360 degrees
So 30*n = 360 so that n = 12.
ANSWER: 12 sides.
What else can I help you with?
How do you calculate one interior angle in a regular polygon?
If the polygon has n sides, each exterior angle is 360/n degrees. The interior angle is its supplement, that is 180 - exterior angle. This is much simpler than trying to remember 180*(n-2)/n degrees.
How many sides of a regular polygon with interior angles of 178?
Interior angles 178 so exterior angles 2. Number of sides of any regular polygon = 360/exterior angle You polygon has 180 sides. Bet you're glad you didn't have to sketch it!
What regular polygon has interior angle 177?
If interior angles are 177o then exterior angles are 3o. Exterior angle times number of sides is always 360 so the polygon has 120 sides.
How many sides does the polygon have if it has an interior angle which is 3 times the exterior angle?
Providing that it is a regular polygon it will have 8 sides.
What is the interior and exterior angle of a regular 15 sided polygon?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nSubstituting with n=15, then the answer is thatthe interior angle = 12x13 =156The measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nSubstituting with n= 15, then the answer is that the exterior angle = 24
What is the sum of the measures of the interior angles of the regular polygon if each exterior measures 120?
Hint: in a regular polygon interior plus exterior = 180o, always.
How do you work out the exterior and interior angles of a regular polygon with W sides?
Exterior angle regular polygon = 360° ÷ number of sides = 360° ÷ W Interior angle regular polygon = 180° - exterior angle regular polygon = 180° - (360° ÷ number of sides ) = 180° - (360° ÷ W)
What is the interior and exterior angle of a regular polygon?
Each exterior angle of a regular polygon with n sides is 360/n degrees. Each interior angle of a regular polygon is 180 - Exterior angle. A direct formula for the interior angle is 180*(n-2)/n degrees.
If the exterior angle of a regular polygon is 20 what is the interior angle of this polygon?
160
What is a term to calculate the angles of any polygon?
There is no term to calculate any angle of any irregular polygon. For a regular polygon with n sides, each exterior angle is 360/n degrees. Each interior angle is (180 - exterior angle).
What is the exterior and interior angle of a regular 10 sided polygon?
Exterior = 36 degrees Interior = 144 degrees
What are the interior and exterior angles of a regular polygon?
If the polygon has n sides, each exterior angle is 360/n degrees.The interior angle is 180 less exterior angle.
What is the answer of the polygon interior angle is five times the size of exterior?
Interior + Exterior = 180 and Interior = 5*Exterior So interior = 150 degrees and exterior = 30 degrees. Nothing more may be said unless it is known that the polygon is regular.
If the sum of the interior angles of a polygon equals the sum of the exterior angles what is the name of the polygon?
A Regular Polygon
What is the size of each interior angle of a regular polygon with 28 sides?
The easiest way to calculate this is to calculate the exterior angle and use the fact that the exterior and interior angles are supplementary. Sum exterior angles = 360° → Each exterior angle of a regular 28-agon is 360° ÷ 28 → Each interior angle of a regular 28-agon = 180° - 360° ÷ 28 = 167 1/7° ≈ 167.14°
Which regular polygon's interior angles is three times that of its exterior angles?
octagon interior=135 exterior=45
What type of regular polygon has equal interior and exterior angles?
A quadrilateral.
