In the figure beside PQ||RS, ∠BPQ=40°, ∠BPR=155° and ∠CRS=70°; let’s write the measurement of all the angles of APR

Given that PQ||RS and ∠BPQ=40° and ∠BPR=155°

Also, ∠CRS=70°

Draw a line through A such that PQ||AY||RS

Since AB is a straight line ,

∠APB=180° (straight angle)

⇒ ∠BPR+∠APR=180°

⇒ 155° +∠APR=180°

⇒ ∠APR=180°-155°

⇒ ∠APR=25°…………..(1)

Since PQ||AY

So, ∠PAY=∠BPQ=40° (corresponding angles)

Similarly, AY||RS

So, ∠RAY=∠CRS=70° (corresponding angles)

Now, ∠PAR=∠PAY+∠RAY=40°+70°=110°

Now, in ∆APR,

∠PAR+∠APR+∠ARS=180°

⇒ 110°+25° +∠ARS=180°

⇒ 135° +∠ARS=180°

⇒ ∠ARS=180°-135°

⇒ ∠ARS=45°

Hence, ∠ARS=45°, ∠PAR=110° and ∠APR=25°