Question

Measure of arc PQ
Write the number only do not put the degree symbol.

Answer 1

∠QAR = 25

∠UAP = 48

∠TAS = 72

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