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What is interior and exterior angle in polygon?
In a polygon, an interior angle is formed by two adjacent sides inside the polygon, while an exterior angle is formed between one side of the polygon and the extension of an adjacent side. For any polygon, the sum of the interior angles can be calculated using the formula ((n - 2) \times 180^\circ), where (n) is the number of sides. Conversely, the sum of the exterior angles of any polygon is always (360^\circ), regardless of the number of sides.
What is the interior and exterior angle of a 18 sided shape?
For an 18-sided polygon (octadecagon), the formula to calculate the interior angle is ((n-2) \times 180° / n), where (n) is the number of sides. Substituting (n = 18), the interior angle is ((18-2) \times 180° / 18 = 160°). The exterior angle can be found using the formula (360° / n), which gives (360° / 18 = 20°). Therefore, each interior angle is 160° and each exterior angle is 20°.
How can you prove that the sum of exterior angles of a polygon is 360 degrees?
With any regular polygon it is 180 minus interior angle times number of sides equals 360 degrees
What is the number of sides in a regular polygon in which the measure of an interior angle is seventeen times the measure of an exterior angle?
The regular polygon has 36 sides. Check: Exterior angle=360/36=10 degrees Interior angle=34*180/36=170 degrees. 170 is 17 times larger than 10 so 36 sides is the correct answer. Method: 180n-360=17*180 180n=6480 n=36
What is the number of sides of a regular polygon in which the measure of an interior angle is seventeen times the measure of an exterior angle?
17x+x=180 degrees as interior+exterior angle = 180 degrees. 18x=180 so x=10, this is the exterior angle. 360/10=36, this is the number of sides. Check: 34*180/36=170 degrees which is 17 times larger than 10 so this answer is correct.
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 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 an equiangular polygon have if the measure of an angle of the polygon exceeds four times the measure of one of it's exterior angles by 30?
Interior angle + Exterior angle = 180 So Interior angle = 180 - Exterior angle Interior angle = 4*Exterior angle + 30 Substitute for Interior angle: 180 - Exterior angle = 4*Exterior angle + 30 Collect like terms: 150 = 5*Exterior angle Divide by 5: Exterior angle = 30 deg Therefore number of sides = 360/30 = 12
How many sides does the regular polygon have if each interior angle measure is four times the measure of each exterior angle measure?
It will have 10 sides and each interior angle measures 144 degrees while each exterior angle measures 36 degrees
How many sides has a regular polygon whose interior angle is 11 times its exterior angles?
The measure of an interior angle in degrees of a regular polygon of n sides is given by the formula: 180 x (n-2) / nThe measure of an exterior angle in degrees of a regular polygon of n sides is given by the formula: 360/nIf the interior angle is 11 times the exterior angle, then:180 (n-2)/n = 11 x 360/nthen: 180 n - 360 = 11 x 360, or180 n = 12 x 360that its solution gives n = 24Accordingly, the answer is that the number of sides of this polygon is 24
How can you prove that the sum of exterior angles of a polygon is 360 degrees?
With any regular polygon it is 180 minus interior angle times number of sides equals 360 degrees
Which regular polygon's interior angles is three times that of its exterior angles?
octagon interior=135 exterior=45
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 is the number of sides in a regular polygon in which the measure of an interior angle is seventeen times the measure of an exterior angle?
The regular polygon has 36 sides. Check: Exterior angle=360/36=10 degrees Interior angle=34*180/36=170 degrees. 170 is 17 times larger than 10 so 36 sides is the correct answer. Method: 180n-360=17*180 180n=6480 n=36
What is the number of sides of a regular polygon in which the measure of an interior angle is seventeen times the measure of an exterior angle?
17x+x=180 degrees as interior+exterior angle = 180 degrees. 18x=180 so x=10, this is the exterior angle. 360/10=36, this is the number of sides. Check: 34*180/36=170 degrees which is 17 times larger than 10 so this answer is correct.
How do you find the exterior angle of a polygon?
360/number of sides 180 times the number of sides the polygon has then minus 360. This gives the total sum of the exterior angles. Then to get the angle of one exterior angle divide it by the number of sides the polygon has.Very easy when you know the formula!
What is the sum of the measures of the interior angles of a regular polygon is each exterior angle measures 120?
To find the sum of the measures of the interior angles of a regular polygon with each exterior angle measuring 120 degrees, we first determine the number of sides in the polygon. The sum of exterior angles of any polygon is always 360 degrees, so the number of sides ( n ) can be calculated as ( n = \frac{360}{120} = 3 ). Since it is a triangle, the sum of the interior angles is given by the formula ( (n - 2) \times 180 ) degrees, which for a triangle (3 sides) is ( (3 - 2) \times 180 = 180 ) degrees. Thus, the sum of the measures of the interior angles is 180 degrees.
