The [tex]\bf{\angle 2}[/tex] and [tex]\bf{\angle 8}[/tex] are the alternate exterior angles.
Further explanation:
If two parallel lines intersected by a third line called as a transversal line, it froms eight angles as shown in Figure 1.
The eight angles will together form four pairs of corresponding angles.
[tex]\angle 1[/tex] and [tex]\angle 5[/tex] constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs.e.g. [tex]\angle3+\angle7[/tex], [tex]\angle2+\angle6[/tex], [tex]\angle4+\angle8[/tex].
Angles that are in the area between the parallel lines like [tex]\angle 4[/tex] and [tex]\angle6[/tex] above are called interior angles whereas the angles that are on the outside of the two parallel lines like [tex]\angle1[/tex] and [tex]\angle8[/tex] are called exterior angles.
Angles that are on the opposite sides of the transversal are called alternate angles.e.g. [tex]\angle1+\angle7[/tex].
All the angles that are either exterior pair of angles, interior pair of angles, alternate pair of angles or corresponding pair of angles are all congruent.
From the given figure, it is observed that the [tex]\angle 1+\angle7[/tex] and [tex]\angle 2+\angle8[/tex] are alternate exterior angles.
Therefore, [tex]\bf{\angle 2}[/tex] and [tex]\bf{\angle 8}[/tex] are the alternate exterior angles.
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Answer Details :
Grade: Senior School
Subject: Mathematics
Chapter: Geometry.
Keywords:
Angle ,interior angle, exterior angles, alternate angles, corresponding angles, transversal lines, parallel lines, triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, angle A, angle B, angle C.
