Answer:
∠QAR = 25
∠UAP = 48
∠TAS = 72
Step-by-step explanation:
- Angles on a straight line add up to 180°
If PS is a straight line, then ∠PAQ + ∠QAR + ∠RAS = 180°
We are told that ∠PAQ = 72 and ∠RAS = 83, so substituting these into the above equation:
72 + ∠QAR + 83 = 180
⇒∠QAR = 180 - 72 - 83 = 25
If QT is a straight line, then ∠PAQ + ∠UAP + ∠TAU = 180°
We are told that ∠PAQ = 72 and ∠TAU = 60, so substituting these into the above equation:
72 + ∠UAP + 60 = 180
⇒∠UAP = 180 - 72 - 60 = 48
Finally, if QT is a straight line, then ∠QAR + ∠RAS + ∠TAS = 180°
We have determined that ∠QAR = 25 and we are told that ∠RAS = 83, so substituting these into the above equation:
25 + 83 + ∠TAS = 180
⇒∠TAS = 180 - 25 - 83 = 72
