M∠Q =
m∠R =
m∠S =

40 POINTS

9514 1404 393

  ∠Q = 89°

  ∠R = 123°

  ∠S = 91°

Step-by-step explanation:

It seems easiest to start by finding the measures of each of the arcs. The measure of an arc is double the measure of the inscribed angle it subtends.

  arc QRS = 2·∠P = 114°

So, ...

  arc QR = arc QRS - arc RS = 114° -41° = 73°

The total of the arcs around the circle is 360°, so ...

  arc PQ = 360° -arc PS -arc QRS

  arc PQ = 360° -137° -114° = 109°

__

  ∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)

  ∠Q = 89°

__

  ∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)

  ∠R = 123°

__

  ∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)

  ∠S = 91°

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

5.25 ounces

step-by-step explanation:

divided 3/4 and 6