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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- Sep 25th 2008, 10:27 PMfabxx[SOLVED] Find the degree of the angles
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!!! - Sep 25th 2008, 10:53 PMMoo
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.