Definition of alternate interior angles helps in understanding the concept about the alternate interior angles. Alternate interior angles are the angles formed when a line (Transversal) crosses two lines that are parallel to each other. They are pair of angles inside the parallel lines and on opposite sides of the transversal. Alternate interior angles are congruent (same). In real life, a good example to understand pairs of angles is a window plane.
From the figure a and b are alternate interior angles.
1 and 2 are alternate interior angles
So, a = b and 1= 2
Example 1: If angle a is 450 and angle 2 is 1350 then what is angle b and angle 1?
Solution: As angle a and angle b are alternate interior angles, they are congruent.
=> So, ∠a =∠b =45°
=> As angle 1 and 2 are alternate interior angles, they are also congruent.
=> So, ∠1 =∠2 =1350
Example 2: If angle 4 = 50 degree, find the measure of angle 2 and angle 3?
Solution: The given angle 4 is equal to 500.
=> Since, Angle 4 is the interior angle and its alternate angle is 2.
=> Therefore, ∠4 = ∠2= 500
=> Another pair of alternate interior angles is angle 1 and 3
=> Angle 4 and 1 lie in the same line. So, sum of their angles = 1800
=> Therefore, 50 + ∠ 1 = 180
=> Then, ∠ 1 = 1300
=> Since angle 1 and 3 are alternate interior angles
=> Therefore, ∠1 = ∠3 = 1300