Question

If two parallel lines are cut by a transversal, then each pair of corresponding angles are _______________.
A) Congruent
B) Obtuse
C) Acute
D) \[{90^ \circ }\]

Answer 1

Hint: Draw a diagram relatable with this with two parallel lines and one transversal then examine each and every case carefully by taking suitable examples.

Complete Step by Step Solution:
Let us try draw the figure first

Clearly in this diagram the blue lines are the parallel to each other and the green line is a transversal and angle A and B are corresponding to each other. Also angle C and D are corresponding to each other.
Now For Option D:
We cannot have \[{90^ \circ }\] each time that is only an special case like also in the figure given clearly none of the angles are \[{90^ \circ }\]. So that settles it option D is incorrect.
For Option C: All corresponding angles cannot be acute to each other like in this case angle A and B are corresponding as well as acute but option C and D are corresponding but obtuse. Therefore option C is also incorrect.
For option B: Much like option C, in this case angle C and D are obtuse as well as corresponding but the angle A and B is corresponding but not obtuse. Therefore option B is also incorrect.
So that leaves us with only one option i.e., Congruent.
Therefore, If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent, which means option A is the correct answer.

Note: Acute angles are the angles which are less than a right angle and obtuse angles are just the opposite i.e., it is an angle which is greater than \[{90^ \circ }\] . Also note that congruent angles are two or more angles that have the same measure. In simple words, they have the same number of degrees. It's important to note that the length of the angles' edges or the direction of the angles has no effect on their congruency. As long as their measure is equal, the angles are considered congruent.