A cyclic quadrilateral ABCD is such that AB = BC, AD = DC and AC and BD intersect at O. If ∠CAD = 46º, then the measure of ∠AOB is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 90º
AD = DC then ∠CAD = ∠DCA = 46°
The sum of the opposite angle of a cyclic quadrilateral will be equal to 180.
∠DAB + ∠DCB = 180
46 + a + 46 + a = 180 (∠BAC = ∠BCA = a)
2a = 88
a = 44
∠BAC = ∠BCA = 44°.
In ADC,
46 + 46 + ∠ADC = 180
∠ADC = 88°
So ∠ABC = 180 - 88 = 92
∠ABD = 92/2 = 46°.
In AOB,
∠AOB + ∠OAB + ∠OBA = 180
∠AOB = 180 - 44 - 46
∠AOB = 90°.