Question

In the adjoining figure, identify the pair of corresponding angles.

Answer 1

Hint:- When two lines intersect by another line, the angles in matching corners are called corresponding angles.


Complete step by step by solution
In the above figure a, b are two parallel lines, which are crossed by a transversal line called c. Line and c form angles$$\text{1},\text{ 2},\text{ 3 and 4}$$. Similarly line b and line c form angles 5,6,7,8.

Now according to hint in the figure $$\text{angle }\left(\text{1},\text{ 3}\right),\text{ angle }\left(\text{2},\text{ 4}\right),\text{ angle }\left(\text{5},\text{ 6}\right)\text{ and angle }\left(\text{7},\text{ 8}\right)$$are corresponding angles.
Therefore, here we have four pairs of corresponding angles, which are$$\left(\text{1},\text{ 3}\right),\left(\text{2},\text{ 4}\right),\left(\text{5},\text{ 6}\right)\text{ and }\left(\text{7},\text{ 8}\right)$$.
As we know corresponding angles are always equal so these four pairs of angles are equal.
So, these four pairs of angles are equal.
i.e. $\mathrm{\angle }1=\mathrm{\angle }3,\mathrm{\angle }2=\mathrm{\angle }4,\mathrm{\angle }5=\mathrm{\angle }6and\mathrm{\angle }7=\mathrm{\angle }8$


Note –If two lines which are crossed by a transversal line are parallel, then the corresponding angles are equal.
Hence, here all corresponding angles are equal.