Question

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PLEASE TELL STEP BY STEP
In triangle ABC, AO and BO are the angle bisectors of A and B respectively.
Find the value of x​

Answer 1

Answer:

Step-by-step explanation:

Since AO and BO are angle bisectors,

∠1 = ∠2    --------------- (1)

∠3 = ∠4  ---------------- (2)

In ΔABC, sum of all angles = 180°

∠1 + ∠2 + ∠3 + ∠4 + 45° = 180

=> 2∠1 + 2∠3 = 135°   ( from ( 1 ) and (2) )

=> ∠1 + ∠3 = 135°/2  -------------- (3)

In ΔAOB,

//sum of all angles is 180°

∠1 + ∠3 + 360 - x = 180°

=> 135°/2 + 360 - 180 = x°  ( from (3))

=> 135°/2 + 180° = x°

=> x° = 495°/2 = 247.5°

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