[SOLVED] Find the degree of the angles

**fabxx** · September 25th 2008, 10:27 PM

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!!!

**Moo** · September 25th 2008, 10:53 PM

Hello,

$\angle AOB=n$

Note that $\angle {\color{red}AOD}=180-n$
But we know that $\angle OAD+\angle ODA+\angle AOD=180$
Hence $\angle OAD+\angle ODA=180-\angle {\color{red}AOD}=180-(180-n)=n$

Similarly, we have $\angle OBC+\angle OCB=n$

Thus the sum of the four angles OAD, ODA, OBC and OCB is 2n.

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