Question

Do not use spaces in your answer. The measure of arc PS is

Answer 1

Hello from MrBillDoesMath!

Answer:

129

Discussion:

Angle PAR = Angle PAS + Angle SAR (*)

Angle PAR = 180 (a straight line has 180 degrees)

Substituting in (*) gives

180 = Angle PAS + Angle SAR

But Angle SAR = 51 (given) =>

180 = Angle PAS + 51 => subtract 51 from both sides

Angle PAS = 180 - 81 = 129

Since PAS is a central angle, measure of the arc PS = measure angle PAS = 129

Note: I'm assuming that arc PS refers to the smaller arc, not arc PQS ( the larger arc). The problem statement is not clear on that point.

Thank you,

MrB