Answer: 12 outcomes total
Check out the diagram below
Edit: I added the tree diagram as well
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Explanation:
I prefer to make a two way table for problems like this. Such diagrams make it fairly clear why multiplication is used when it comes to probability and counting problems.
Check out the diagram below.
The table has 6 rows and 2 columns.
The 6 rows represents the outcomes 1 through 6 on the number cube.
The 2 columns represent the outcome of heads (H) vs tails (T)
Inside the 6*2 = 12 inner cells, we'll have each outcome.
For example, the upper left corner has H1 to mean "flipped heads and got a 1 on the number cube". The next cell over is T1 to mean "tails on the coin, 1 on the number cube". The rest of the table is filled out in this manner.
Check the picture below.
so, bearing in mind that vertical angles are equal, thus ∡AED = ∡BEC, and we know that ∡BEC = 52 = ∡AED, so those two angles added up are 104°.
now, a circle has a total of 360°, if we take away those 104° from the red angles, what's leftover is just 256°, well, the green angles there are also vertical angles and thus twins, so each one will take half of 256°.
∡BEA = 128° = ∡CED.
