Let me see if I can help you with this one (it's not too difficult!!)
Since it's a rhombus, all sides are equal, so AB = DC = 21
Since m < ABE = 60,, then the m < BDA = 60 also, because BAD is a triangle with two sides equal (BA, DA). And from a theory in geometry, when a triangle has two equal sides, the angles opposite those sides are equal, too. Then, because we have a triangle with two 60 degree angles, the remaining angle (BAD) is 60, too. So, all sides of triangle BAD are equal. Thus, AB = BD = 21. And since AE bisects BD, then DE = (!/2) * 21 = 10.5.
Well, so what?? How does this help us find CE?? Well, the diagonals of a rhombus intersect at right angles, so triangle CED is a right triangle with < CED being the right angle. and CD the hypotenuse. And we know two sides of this triangle (DE = 10.5 and CD =21). And by the Pythagorean theorem, CE = SQRT (21^2 - 10.5^2) = 18.2 (rounded).
To find the m < BAC, note that EA bisects < BAD, and since < BAD was found to be 60, then m < BAC = 30.
To find m < BCE, note that in triangle ABC, sides AB = BC, so the angles opposite those sides are equal, too. Thus, m < BAC = m < BCA = m < BCE = 30.
We've established that the diagonals form right angles, so m < BEC = 90.
I think that's what you wanted to know (hopefully). If you have any questions about this, feel free to post them. I hope my explanations were clear!!
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