Question

Lines $l$ and $m$ and lines $a$ and $b$ are parallel to each other. How many pairs of corresponding angles are formed in the figure given below?

Answer 1

When two parallel lines are intersected by a third line (transversal), the angles that occupy the same relative position at each intersection are called corresponding angles.

Let's name the angles formed by transversal lines $aandb$ and parallel lines $landm$.

The figure is depicted below.

Here, the pairs of corresponding angles are:

• $\angle 1and\angle 5$
• $\angle 2and\angle 6$
• $\angle 3and\angle 7$
• $\angle 4and\angle 8$
• $\angle 9and\angle 13$
• $\angle 10and\angle 14$
• $\angle 11and\angle 15$
• $\angle 12and\angle 16$

Similarly, let's name the angles formed by transversal lines $landm$ and parallel lines $aandb$.

Here, the pairs of corresponding angles are:

• $\angle 1and\angle 9$
• $\angle 2and\angle 10$
• $\angle 3and\angle 12$
• $\angle 4and\angle 11$
• $\angle 5and\angle 13$
• $\angle 6and\angle 14$
• $\angle 7and\angle 15$
• $\angle 8and\angle 16$

$\therefore$ A total of 16 pairs of corresponding angles would be formed by the given tansversal and parallel lines.