Let us write the angle derived from the equation x = y in the positive direction of x - axis.

x = y

Putting different values of x, we get different values of ‘y’, hence we get points for plotting as:

Now we need to find the angle line derived from line y = x in the positive direction of x - axis i.e. ∠ADB

From the graph, clearly ABD is a right - angled triangle, therefore

∴ ∠DAB = 90°

And

AD = AB

∠ABD = ∠ADB [angles opposite to equal sides are equal]

Also, In ΔABC By angle sum property of triangle

∠DAB + ∠ABD + ∠ADB = 180°

⇒ 90° + ∠ABD + ∠ABD = 180°

⇒ 2∠ABD = 90°

⇒ ∠ABD = 45°