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!!!
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.