BE and CD are both diameters of circle with center A (see fi

my approach differs from what Manhattan had done and so I need some clarification, please.

What I did was:

1. Given that area of circle is 180 and that BE, CD are both diameters
2. I found the area of ACB sector using the angle 40% and got it as 20 sq.units
3. I then figured out BAD area by 90 - 20 (because C-B-D-C is a semi circle)
4. I then figured out ACE area by 90 - 20 (because C-B-E-C is a semi circle)
5. I then figured out ADE area by 90 - 70 (because C-D-E-C is a semi circle)

so, the total is 20 + 20 = 40

However, Manhattan says "The two central angles, CAB and DAE, describe a total of 80°."

What I do NOT understand is, how can we say that Angle EAD = Angle BAC ?

Is it something like, when two diameters intersect, the opposite angles formed by them are equal? I am not sure of this but looks like could have saved a few seconds in solving this.

EDIT: FOUND IT! Angle EAD = Angle BAC because vertical angels are equal. The next chapter "Lines & Angles" gave it away