The correct option is C 135∘
Since, AB||CD, therefore,
∠BTV=∠DVS=45∘ [Pair of Corresponding angles]
Also, RS is s straight line and hence,
∴∠BTV+∠PTB+∠RTP=180∘ [Sum of angles on a line is 180∘]
⇒∠RTP=180∘−(45∘+55∘)
⇒∠RTP=80∘...(i)
Also, ∠RTA=∠BTV=45∘ [Vertically opposite angles]
Hence, ∠TUC=∠RTA=45∘ [ [Pair of Corresponding angles]
Now, ∠TUC+∠CUQ=180∘ [Linear Pair]
⇒∠CUQ=180∘−45∘=135∘...(ii)
From (i) and (ii)
∠CUQ+∠RTP=80∘+135∘=215∘