What is exterior inequality theorem?
Geometry. The exterior angle of a triangle will always be greater than the two remote interior angles. In other words, the measure of the red angle is greater than that of the blue angle or the green angle.
What is the formula for the exterior angle theorem?
The exterior angle theorem tells us that any exterior angle of a triangle equals the sum of the opposite two interior angles and that the sum of all three interior angles of a triangle equals 180° , the sum of two right angles (triangle sum theorem).
What is the rule for exterior angles of a triangle?
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). This is also known as the Exterior Angle theorem. The sum of all the exterior angles of a triangle is 360°.
What is triangle inequality theorem?
triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
What is the sum of the three exterior angles of a triangle?
One can also consider the sum of all three exterior angles, that equals to 360° in the Euclidean case (as for any convex polygon), is less than 360° in the spherical case, and is greater than 360° in the hyperbolic case.
How does the triangle inequality theorem relate to angles?
Theorem 36: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side.
How do you find the sum of exterior angles?
The sum of the exterior angles of a regular polygon will always equal 360 degrees. To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has.
How do you calculate exterior angles?
– The measure of each exterior angle is 360°/n – Sum of exterior angles of a polygon is ∠a’ + ∠b’ + ∠c’ + ….. + ∠n’ = 360°. – The sum of the exterior angles is 360°.
How to solve for an exterior angle?
Sum of exterior angles of a polygon. The sum of the exterior angles of any polygon is always equal to 360°.
What is the formula for alternate exterior angles?
∠1, ∠2, ∠7, ∠8 are the alternate exterior angles Alternate Angles Theorem Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
What is the definition of exterior angle theorem?
The exterior angle theorem states that the exterior angle formed when you extend the side of a triangle is equal to the sum of its non-adjacent angles. Remember, our non-adjacent angles are those that don’t touch the angle we are working with.