The measures for the lengths angles of the rectangle PQRS with diagonals PR and QS are:
a. SQ = 24
b. PR = 24
c. m∠QPR = 23°
d. m∠PSR = 90°
e. m∠SQR = 67°
f. m∠PTQ = 134°
A rectangle has two diagonals that are the same(congruent) and they bisect each other so ST = QT and;
SQ = 2 × 12 = 24
Also, PR = SQ so SQ = 24.
The rectangle have two pair of parallel sides which makes the angles formed by its diagonals alternate angles.
Given that m∠PRS = 23, then m∠QPR is also equal to 23° because they are alternate interior angles.
And each interior angle of the rectangle is equal to 90° so m∠PSR is equal to 90°.
PTQ forms an Isosceles triangle with one base angle equal to 23° so;
m∠PTQ = 180 - 2(23)
m∠PTQ = 134°
Thus the properties of a rectangle and it's diagonals have helped to find the lengths and angles as SQ = 24, PR = 24, m∠QPR = 23°, m∠PSR = 90°, m∠SQR = 67° and m∠PTQ = 134°.