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

∠TOS=20°
∠POQ=60°
∠POT=?
∠ROP=?
∠QOS=?

Question

Let’s try to write the measurement of the angles from the figure given below:∠TOS=20° ∠POQ=60° ∠POT=?∠ROP=?∠QOS=?

Philoid · Accepted Answer

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

∠ROQ is lying opposite to ∠POS.

So, our first pair of vertically opposite angles is ∠ROQ and ∠POS.

∠ROP is lying opposite to ∠QOS.

So, our second pair of vertically opposite angles is ∠ROP and ∠QOS.

Vertically opposite angles are equal.

So ∠ROQ = ∠POS

and ∠ROP = ∠QOS.

Sum of all vertically opposite angles is 360°.

∠ROQ + ∠POS + ∠ROP + ∠QOS = 360°.

Now in the above question,

∠POS = ∠POT + ∠TOS

∠ROQ = 60°.

∠TOS = 20°

So ∠POS = ∠ROQ = 60°.

∠POT = ∠POS - ∠TOS

= 60 – 20

= 40°.

Let ∠ROP = ∠QOS = x [as ∠QOS = ∠ROP……… vertically opposite angles]

So, 60° + 60° + x + x = 360°

120° + 2x = 360°

2x = 360 – 120

2x = 240

x = 240 / 2

x = 120°

So ∠QOS = ∠ROP = 120°.