In diagram arc BC is three times larger than arc AD and angle BEC = 80. Let angle ABD = x and find x.
Here i cannot include the given information into the question. So using the 80 alone, i cannot get any angles...
We know that $\displaystyle 2m\left( {\angle BEC} \right) = m\left( {arc(DA)} \right) + m\left( {arc(BC)} \right)$.
So what is $\displaystyle m\left( {arc(DA)} \right)?$
We know that $\displaystyle 2m\left( {\angle ABD} \right) = m\left( {arc(DA)} \right)$.
I have no idea malaygoel how to proceed from there. That was the original information i know. Could you please expand on that? For i think thats the method the question wants the students to develop.
Also plato, really sorry, but i cant understanding your use of symbols. Wha is m?
Well mabey. But i do think since i am in a different part of the world, that different symbology apply to same meaning.
But without going into that, i am still very interested in what m means. I understanding arc and angle. Considering what you are saying, you might be right. Then i would assume that a easier, more fundemental approach to this question was suitable.
Let O be the center of the circle
It is given that
$\displaystyle \angle{BOC} = 3\angle{AOD}$
Now $\displaystyle \angle{BOC} = 2 \angle{BAC}$
and $\displaystyle \angle{AOD} = 2\angle{ABD}$
But $\displaystyle \angle{BAC} + \angle{ABD}= 80 degrees$
Substitute the values and find angle ABD.
m[angle ABC] means "measure" of angle ABC: always thought that was silly and misleading.
Like for line AB = x, we don't use m[line AB] = x; so why treat angles differently?
That's my opinion: I respect yours, but if it's not same as mine, then it's wrong