Interior Angles Theorem

They sum up to 180.

Interior angles theorem. Interior angles of a polygon. In the above figure l 1 and l 2 are parallel and l is the transversal. Once you can recognize and break apart the various parts of parallel lines with transversals you can use the alternate interior angles theorem to speed up your work.

Here the angles 1 2 3 and 4 are interior angles. The sum of the interior angles 2n 4 right angles. The high school exterior angle theorem hseat says that the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle remote interior angles.

The consecutive interior angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles is congruent. Take any point o inside the polygon. The consecutive interior angles theorem states that the two interior angles formed by a transversal line intersecting two parallel lines are supplementary i e.

So in the picture the size of angle acd equals the size of angle abc plus the size of angle cab. The alternate interior angles theorem states that if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent. Angles cosine rule cube numbers cube root cumulative probabilities cyclic quadrilaterals definite integration de moivre s theorem denary density depreciation difference of two squares differential equations differentiation direct proportion distributive law dividing algebraic fractions dividing decimals.

In a polygon of n sides the sum of the interior angles is equal to 2n 4 90. Abcde is a n sided polygon. The angles that lie in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles.

The sum of all of the interior angles can be found using the formula s n 2 180. Below is the proof for the polygon interior angle sum theorem. Polygons interior angles theorem.