Question

In triangle ABC, m∠ACB = 42°. The angle bisectors AD and BE intersect at point O so that AE + OE = AB. Find m∠A and m∠B.

Answer 1

∠ABC = 84°

∠CAB = 54°

Explanation:

Assume that a point on side AB, its point F

so that, EA = FA

Then triangle AEO ≅ triangle AFO

So,

OF = OE = BF

Triangle BOF is isosceles.

∠CEO=180−∠ABC

So that,

180 −
`(1)/(2)`∠ABC + 42 = 180

Now solve for ∠ABC.

∠ABC = 84°

∠CAB = 180 - 84 - 42 = 54°

That's the final answer.