Geometry Problems |Angle Sum Property | Exterior Angle Property | Find X and Y | Concept Clarification
In this video, Geometry Problems are explained.Many student face difficulties in solving geometrical problems. This video helps to clear their concept and scored good marks as well as positive knowledge
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Angle Sum Property
The angle sum property of a triangle states that the sum of the angles of a triangle is equal to 180º. A triangle has three sides and three angles, one at each vertex. Whether a triangle is an acute, obtuse, or a right triangle, the sum of its interior angles is always 180º.
The angle sum property of a triangle is one of the most frequently used properties in geometry. This property is mostly used to calculate the unknown angles.
What is the Angle Sum Property?
According to the angle sum property of a triangle, the sum of all three interior angles of a triangle is 180 degrees. A triangle is a closed figure formed by three line segments, consisting of interior as well as exterior angles. The angle sum property is used to find the measure of an unknown interior angle when the values of the other two angles are known. Observe the following figure to understand the property.
Angle Sum Property of a triangle
Angle Sum Property Formula
The angle sum property formula for any polygon is expressed as, S = (n − 2) × 180°, where 'n' represents the number of sides in the polygon. This property of a polygon states that the sum of the interior angles in a polygon can be found with the help of the number of triangles that can be formed inside it. These triangles are formed by drawing diagonals from a single vertex. However, to make things easier, this can be calculated by a simple formula, which says that if a polygon has 'n' sides, there will be (n - 2) triangles inside it. For example, let us take a decagon that has 10 sides and apply the formula. We get, S = (n − 2) × 180°, S = (10 − 2) × 180° = 10 × 180° = 1800°. Therefore, according to the angle sum property of a decagon, the sum of its interior angles is always 1800°. Similarly, the same formula can be applied to other polygons. The angle sum property is mostly used to find the unknown angles of a polygon.
Important Points
The following points should be remembered while solving questions related to the angle sum property.
The angle sum property formula for any polygon is expressed as, S = ( n − 2) × 180°, where 'n' represents the number of sides in the polygon.
The angle sum property of a polygon states that the sum of the interior angles in a polygon can be found with the help of the number of triangles that can be formed inside it.
The sum of the interior angles of a triangle is always 180°.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon. The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle. To apply the theorem, we first need to identify the exterior angle and then the associated two remote interior angles of the triangle.
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