x = 8
PR = 18
measure of angle PQT = 30°
Explanation:
The parallel sides of a parallelogram are congruent. SO we equate them together.
20 is parallel to 4x - 12
20 = 4x - 12
add 12 tio both sides
20 + 12 = 4x
32 = 4x
32/4 = 4x/4
x = 8
The diagonals bisect each other at the center. Thus dividing it equally.
PR is divided into two equally:
5y - 36 is congruent to y
5y - 36 = y
collect like terms:
5y - y = 36
4y = 36
4y/4 = 36/4
y = 9
PR = 5y - 36 + y
PR = 6y - 36
PR = 6(9) - 36
PR = 18
Since the diagonals bisect the angles at the 4 corners. The angles at each corner are divided into equal halves.
angle PQR is divided into two equal parts. on eo f the angle is given as 30°.
angle PQT = angle RQT
angle RQT = 30°
Hence, angle PQT is 30°
