a) Here is a rough diagram of two angles with one point in common:
A
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C----B
b) Here is a rough diagram of two angles with two points in common:
A----B
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\/
C
c) Here is a rough diagram of two angles with three points in common:
A----B
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C
d) Here is a rough diagram of two angles with four points in common:
A----B
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C
e) Here is a rough diagram of two angles with one ray in common:
A----B----C