Answer:
Hi, you didn't include the diagram for this question but please find it in the attachment.
PT = TR = TQ = 12
SQ = PR = 24
m∠QSR = m∠QPR = 23°
m∠STR = m∠PTQ = 134°
m∠SQR = 67°
Step-by-step explanation:
ST = 12 (given)
m∠PRS = 23° (given)
Now for the measures
TQ = ST = 12 (Reason is that point T represents a perpendicular bisector)
PT = TR = 12 (Diagonal SQ and PR are of the same length)
SQ = ST + TQ = 12 + 12 = 24
SQ = 24
PR = SQ = 24
m∠QPR = m∠PRS = 23° (alternate angles)
m∠PSR = 90° (right angle)
m∠QSR = 23° (base angles of an isosceles triangle)
m∠STR + m∠QSR + m∠PRS = 180° (sum of angles in a triangle)
m∠STR + 23° + 23° = 180°
m∠STR = 180° - 46° = 134°
m∠PTQ = m∠STR = 134° (vertically opposite angles)
m∠SQR + m∠QRS + m∠QSR = 180° (sum of angles in a triangle)
m∠SQR + 90° + 23° = 180°
m∠SQR = 180° - 113° = 67°
