The angle measured below is 290⁰.Is it possible to get a polygon with an interior angle of 290⁰? Explain your answer
No, it is not possible to have a polygon with an interior angle of 290°.
In a polygon, the sum of all interior angles is equal to (n-2) * 180°, where n is the number of sides. For example, in a triangle (n=3), the sum of all interior angles is (3-2) * 180° = 180°.
In order for a polygon to have an interior angle of 290°, it would need to have a sum of interior angles greater than 180° for each side. However, the sum of interior angles in any polygon is always less than 180° times the number of sides. Therefore, it is impossible to have a polygon with an interior angle of 290°.
No, it is not possible to have a polygon with an interior angle of 290⁰.
In a polygon, the sum of all interior angles is given by the formula (n-2) * 180⁰, where n represents the number of sides or vertices of the polygon. To find the measure of each interior angle, we divide this sum by the number of sides.
For example, let's consider a triangle (n = 3). The sum of its interior angles would be (3-2) * 180⁰ = 180⁰, and each interior angle would measure 180⁰/3 = 60⁰.
If we apply the formula to a quadrilateral (n = 4), we get (4-2) * 180⁰ = 360⁰. Therefore, each interior angle would have a measure of 360⁰/4 = 90⁰.
For any polygon, the measure of each interior angle must be less than 180⁰. Since 290⁰ is greater than 180⁰, it is not possible to have a polygon with an interior angle of 290⁰.