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Answer:
a) ADC
b) ABC
c) ACB
d) CAD, DAB
e) CDm, BDA
f) ABD
Explanation:
a) Any of the letters on lines going through point D could be used to name an angle with DC as one side. (Letters s and C would name an angle of measure zero, so might not be of interest.)
∠ADC has side DC
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b) Any angle name with B in the middle will have B as its vertex.
∠ABD is an angle with vertex B
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c) Ray CE is coincident with ray CD, so ...
∠ACE is another name for ∠ACD
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d) Adjacent angles share a side, typically between the two angles. A linear pair of angles will be adjacent angles.
∠BAD and ∠CAD are adjacent angles
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e) In order to properly name a pair of vertical angles, we need to be able to name two sets of opposite rays that share end points. Opposite rays emanate from points C and D, but no named points are seen outboard of those intersections. If we use 'm' as the name of a point on line m, then we can say a pair of vertical angles is ...
CDm and BDA are two vertically opposite angles
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f) The supplement to EBD will be the other angle that makes a linear pair with angle EBD. It is defined using point A on the ray opposite ray BE.
∠ABD is the supplement of ∠EBD