Question

If line segment RS is parallel to line segment MN, then the value of a is

Answer 1

34, the two angles are corresponding. theyre mirrors of eachother 

Answer 2

Answer: The correct option is

(B) 74 because ∠TRS and ∠TMN are corresponding angles.

Step-by-step explanation: Given that the line segment RS is parallel to the line segment MN.

We are to find the value of a.

From the figure, we note that

RS is parallel to MN and TM is a transversal.

So, we get

`m\angle TRS=m\angle TMN~~~~~~~~\textup{[corresponding angles]}`

Now,

`m\angle TMN=m\angle TMS+m\angle SMN\\\\\Rightarrow m\angle TMN=40^\circ+34^\circ\\\\\Rightarrow m\angle TMN=74^\circ.`

Therefore, we get

`m\angle TRS=a^\circ=74^\circ\\\\\Rightarrow a=74.`

Thus, the value of a is 74, because ∠TRS and ∠TMN are corresponding angles.

Option (B) is correct.