In the figure below, what is the sum, in terms of n, of the degree measure of the four angles marked with question marks (?)
a) n
b)2n
c) 180-n
d) 360-n
e)360-2n
- - - - -615
Please show steps so I can understand. Thanks in advance!!!
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In the figure below, what is the sum, in terms of n, of the degree measure of the four angles marked with question marks (?)
a) n
b)2n
c) 180-n
d) 360-n
e)360-2n
- - - - -615
Please show steps so I can understand. Thanks in advance!!!
Hello,
$\displaystyle \angle AOB=n$
Note that $\displaystyle \angle {\color{red}AOD}=180-n$
But we know that $\displaystyle \angle OAD+\angle ODA+\angle AOD=180$
Hence $\displaystyle \angle OAD+\angle ODA=180-\angle {\color{red}AOD}=180-(180-n)=n$
Similarly, we have $\displaystyle \angle OBC+\angle OCB=n$
Thus the sum of the four angles OAD, ODA, OBC and OCB is 2n.