Answer:
1: a. x=120, b. x=19, 2: mOPR=137, mSRQ=140, mPQT=83
Explanation:
1.
a. since x is an exterior angle, we know x is the sum of the other 2 interior angles. the box in the corner means that angle is a right angle, or 90 degree angle. so x = 90 + 30, s=120
b. again, 103 is an exterior angle so 103 = 47-x +2x+38. simplify to get 103 = x+84, so x=19
2.
OPR is an exterior angle so mOPR = mPQR + mPRQ, or 2y+15 = 97 + y-21. simplify and solve for y to get y=61. plug this into 2y+15 to get mOPR = 137.
because SRQ is an exterior angle, it equals RPQ + PQR. first we need to find RPQ. since PQR is a triangle, PQR + PRQ + RPQ = 180. PRQ = y-21 = 40. so RPQ=180-97-40 = 43. so SRQ = 43+97 = 140. (you could also use the fact that PRQ + SRQ = 180)
the exterior angles added up together = 360, so OPR + SRQ + PQT = 360. plug in the known values to get PQT = 360 - 137 - 140 = 83