As per the reference image attached hereby along with the question statement,
(1) (∠4 and ∠6) are a pair of alternate exterior angles,
(2) (∠16 and ∠10) are a pair of alternate interior angles,
(3) (∠11 and ∠16) are a pair of consecutive interior angles,
(4) (∠12 and ∠14) are a pair of alternate exterior angles, and finally,
(5) (∠7 and ∠13) are a pair of alternate interior angles
As per the reference image attached hereby along with the question statement, we are provided with two pairs of parallel lines that intersect each other, namely AB, CD, EF and GH (As shown in the attachment attached hereby at the end of this answer), and these pairs form 16 angles, which as numbered from 1 to 16, as their individual denotion.
We are required to determine the relation between the following pair of angles:
(1) ∠4 and ∠6
(2) ∠16 and ∠10
(3) ∠11 and ∠16
(4) ∠12 and ∠14
(5) ∠7 and ∠13
(1) Starting with the first pair (∠4 and ∠6), they are formed outside the parallel lines (EF and GH), due to the transversal AB, at opposite corners of two consecutive intersection points, hence these two are a pair of alternate exterior angles.
(2) Similarly (∠16 and ∠10) are a pair of alternate interior angles, as they are formed in between the parallel lines (EF and GH), due to the transversal CD, at alternate locations of two consecutive intersection points.
(3) (∠11 and ∠16) are a pair of consecutive interior angles, as they are formed in between the parallel lines (EF and GH), due to the transversal CD, at the same location in consecutive intersection points.
(4) (∠12 and ∠14) are a pair of alternate exterior angles, as they are formed outside the parallel lines (EF and GH), due to the transversal CD, at opposite corners of two consecutive intersection points.,
(5) And lastly, (∠7 and ∠13) are a pair of alternate interior angles, as they are formed in between the parallel lines (AB and CD), due to the transversal EF, at alternate locations of two consecutive intersection points.
- Angle: In Euclidean Geometry, an angle is an open, planar figure formed by two rays, being called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
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