Question

ABCD is a square. Diagonals AC and BD intersect at O. State the measure of angle AOB

Answer 1

measure of angle AOB is equal to 90 degree
as diagonal of a square bisect each other at 90°

Answer 2

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Here is your answer:

In ΔAOB and ΔCOB,

AB = BC (we know that the sides of the square are equal)

BO = BO (Common)

OA = OC (The diagonals of square will bisect with each other)

ΔAOB ≅ ΔCOB (SSS)

∠AOB = ∠COB [CPCT]

∠AOB + ∠COB  = 180° (this is the linear pair)

∠AOB + ∠AOB = 180°

∠AOB = 90°