Condition: A pair of alternate exterior angles are complementary.
Co-planar lines are those lines which are in single plane. For example
if there are two lines AB and CD so for co-planar lines both lines must be in a single plane. Such that it can be in XY or YZ or ZX, any one of the plane.
Also,
Complementary Angles: If the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.
Supplementary Angles: Supplementary angles are those angles that sum up to 180 degrees.
Congruent Angles: Congruent angles are the angles that have equal measure.
Refer the figure attached to the answer:
In figure, Angles D, B, E and F are interior angles. Angles A, C, H and G are exterior angles. Angles (D, F) and (B, E) are alternate interior angles.
Now, Looking up the options:
A) A pair of alternate interior angles are congruent.
that means Angle B and E are congruent.
B) A pair of co-interior angles are supplementary.
that means Angle B + F = 180 degree.
C) A pair of corresponding angles are congruent.
that means Angle C and E are congruent.
D) A pair of alternate exterior angles are complementary.
that means Angle A+H=90 degree
After looking all the option A), B) and C) all represents that the lines can be parallel but D) does not indicate that the lines can be parallel.
Hence, A pair of alternate exterior angles are complementary condition does not satisfy that the two lines are parallel.
Learn more about "Supplementary, Complementary and Congruent angles" from here: https://brainly.com/question/928628
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Disclaimer: The question given was incomplete on the portal. Here is the complete question.
Question: Two coplanar lines are cut by a transversal. Which condition does NOT guarantee that the two lines are parallel.
A) A pair of alternate interior angles are congruent.
B) A pair of co-interior angles are supplementary.
C) A pair of corresponding angles are congruent.
D) A pair of alternate exterior angles are complementary.
