Question

If PQ||RS and QR||TS, then find the value of a ​

Answer 1

Answer:

95°

Step-by-step explanation:

In given figure, PQ parallel to RS and segment RQ is a transversal.

∴∠PQR−∠QRS=85

o

....(1) [ Alternate interior angles ]

Also, RQ parallel to TS and segment RS is a transversal.

∴∠QRS−∠TSR=85

o

....(2) [ Alternate interior angles ]

Now, RS is a straight line.

∴∠RST+a=180

o

[ Linear pair ]

⇒85

o

+a=180

o

⇒a=180

o

−85

o

⇒a=95

o

Answer 2

$\huge\red{A}\pink{N}\orange{S}\green{W}\blue{E}\gray{R}$

Given properties - PQ||RS and QR||TS

It is said to find the value of ∠a

∠RQP = 85°

∠QRS = 85° (property of alternate angles)

∠TSR = 85° (property of alternate angles)

So, ∠a + 85° = 180° (property of linear pair)

∠a = 180° - 85°

∠a = 95°

Hence ∠a is 95° (property of linear pair).