Consecutive interior angles are pairs of angles on one side of a line that crosses two other lines, known as co-interior or same-side interior angles. They are formed when a transversal line cuts through two parallel lines and is within the inner region of the polygon. If two lines and a transversal form consecutive interior angles that are supplementary, then the two lines are parallel.
To prove the Consecutive Interior Angle Theorem, use the following steps: ABCD; ∠1 ≅ ∠5; m∠1. Since the transversal line crosses a pair of parallel lines, the consecutive interior angles theorem can be used. This means that when we add the two consecutive interior angles their sum is equal to 180 degrees.
Consecutive interior angles are formed on the inner sides of the transversal and are also known as co-interior angles or same-side interior angles. The angle measure of a polygon is 180 minus the measure of its adjacent interior angle, called a, for each side. When two lines and a transversal form consecutive interior angles that are supplementary, then the two lines are parallel.
If any one of the angles is given, we can easily find the other consecutive angle by subtracting the given angle from 180.
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