Question

in the given square PQRS, PR and QS are the diagonals bisect each other at O. find the value of a and b.?

solve it properly with explaintion.




see figure in attachment​

Answer 1

Answer:

it will be 45°. as the diagnol bisect at 90 degree and according to the triangle property a + b + angle o is equals to 180 degree angle A and b will be equal as it is bisected by equal lines hence by solving A and b will be 45 degree

Answer 2

PQRS is a square therefore,

Angle(POQ) = Angle(QOR) = Angle(ROS) = Angle(SOP) = 90°

Also, PO = QO => ∆(POQ) is an isosceles type of triangle.

=> Angle(OPQ) = Angle(OQP) = x (let)

Hence, Angle(OPQ) + Angle(OQP) + Angle(POQ) = 180° ..........(Angle Summation)

=> x + x + 90° = 180°

=> x = 45°

Also, Angle(a) + angle(x) = 90° .......(Squaretain angle)

=> a° + x° = 90°

=> [a° = 45°]

Similarly, we can calculate that [b° = 45° ]

Hence, the angles a and b measures 45° each.