Question

If pqrs is a rectangle, st=12,and m angle prs =23,find each measure

Answer 1

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°