Question

(4) In the given figure rectangle MNOP is a cyclic quadrilateral. If Angle P 4x +12, and Angle N=3x +28 then find the value of x and also the measures of Angle P and Angle N

Answer 1

In a cyclic quadrilateral...the opposite angles add up to 180 or are supplementary.

Therefore,angle P +Angle N=180
4x+12+3x+28=180
7x+40=180
7x=140
X=20


Angle N=88
Angle P=92.


Hope this helps you a lot...Good luck ahead.

Answer 2

sum of angles in quadrilateral is 360 . and opposite angles is 180 .so 4x+12+3x+28 = 180
then x = 20
angle p is 92 and angle N is 88