Question

3.4. In Fig. 24, PQ and RS are line segments on / and m, respectively. If PQ || RS and QR || TS, find angle a

Answer 1

Answer:

95°

Step-by-step explanation:

If we take line m and l parallel and take RQ as a traversal line.

Angle PQR and QRS become alternate-interior angles. Alternate-interior angles are always equal.

So, QRS=85°

Now if we take RQ and TS as parallel lines and line m as transversal line. Then Angle QRS and RST become alternate-interior angles. So, RST=85°

If we take RST and angle a as linear pair, their sum will be 180°

If RST= 85°

a=180° - 85°

a=95°

Answer 2

Answer:

95°

Step-by-step explanation:

if PQ║RS and QR║TS, then by alternate interior angles,

angle PQR = angle QRS = 85°

and angle QRS = angle TSR = 85°

By linear pair anxiom,

angle TRS + angle a = 180°

⇒ 85° + a = 180°

⇒ a = 180° - 85°

⇒ a = 95°