PQRS is a rectangle and its diagonal PR and QS intersect at O.if angle POQ=110 find the measure of
- angle PQO
- angle PSQ
- angle ORS
P S
Q R
PQRS is a rectangle in which O is the intersection point of both the diagonals PR and QS
We have angle POQ= 110®
Now we need to find out , anglePQO and angle PSQ
As we know in rectangle both the diagonals are equal
So, PR = QS
Also diagonals bisect each other
So PO = QO
Hence, anglePQO = angleOPQ ……………1
Now in triangle POQ ,
AnglePQO + anglePOQ + angleOPQ = 180®
anglePQO + 110 + anglePQOc = 180 (from eqn 1)
2 anglePQO = 180-110
anglePQO = 70/2 = 35®
now , in triangle PQS
anglePQS + angleQPS +anglePSQ = 180
35 + 90 + anglePSQ = 180
125 + anglePSQ = 180
anglePSQ = 180-125 = 55® ans