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and 
are the lengths of two sides of a triangle, which of the following can be the length of the third side?
and 
. Since 
, that means that 
is not an option. It also means that the third side must be less than the sum of 
and 
. Since 
, that rules out 
as an option. You know that the third side must be greater than 
and less than 
: only 
, option II, fits.
, what is the value of 
?
for angle 
, you should notice that even though there are two angles remaining to solve for within triangle ABC, those two angles each equal the same thing. So since the sum of all three has to be 
, and angle a already accounts for 
, 
has to equal the remaining 
. 
means that 
. And then you get to use the same logic all over again. Within triangle BCD, you know that 
and that the sum of the three angles must be 
. That means that 
, so 
.
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