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.

∠ABC = 84°

∠CAB = 54°

Step-by-step 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 − ∠ABC + 42 = 180

Now solve for ∠ABC.

∠ABC = 84°

∠CAB = 180 - 84 - 42 = 54°

That's the final answer.

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1,407.5 hours

step-by-step explanation:

we first convert all the time to hours and then sum them up.

there are 24 hours in 1 day, in 58 days, there are 24 x 58 = 1,392 hours.

there are 60 minutes in 1 hour, thus, 30 minutes will be equivalent to 30 / 60 = 0.5 hours.

therefore, the number of hours it will take mercury to complete a full rotation is 1,392 + 15 + 0.5 = 1,407.5 hours