Let’s try to write the measurement of the angles from the figure given below:

∠1=35°
∠2=?
∠3=?
∠4=?

write.

In the above given figure, let us understand the pairs of vertically opposite angle.

∠1 and ∠3 are lying opposite to each other [in common language lying face to face to each other].

So, first pair of vertically opposite angles is ∠1 and ∠3.

∠4 and ∠2 are also lying opposite to each other.

Hence ∠4 and ∠2 forms our second pair of vertically opposite angles.

Vertically opposite angles are always equal.

Hence ∠1 must be equal to ∠3 and ∠4 must be equal to ∠2.

Also, we know that sum all vertically opposite angles is 360°.

∠1 + ∠2 + ∠3 + ∠4 = 360°.

Now in the question it is given that,

∠1 = 35°

So ∠3 must be equal to 35° [as ∠3 = ∠1……… vertically opposite angles]

Let ∠2 = ∠4 = x [as ∠4 = ∠2……… vertically opposite angles]

So, 35° + 35° + x + x = 360°

70° + 2x = 360°

2x = 360 – 70

2x = 290

x = 290 / 2

x = 145°

So ∠2 = ∠4 = 145°.