I can't find the missing angles.

- anonymous

I can't find the missing angles.

- schrodinger

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- anonymous

|dw:1437537537663:dw|

- anonymous

It is 60 and 60

- anonymous

My textbook says that angle ABC=111 and angle CDE=129

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## More answers

- anonymous

That is the answer but how do i get it?

- mathstudent55

ABCDE is a pentagon.

- mathstudent55

A pentagon has 5 sides.
The sum of the measures of the internal angles of a pentagon is
(n - 2)180 = (5 - 2)180 = 3(180) = 540

- mathstudent55

|dw:1437538174022:dw|

- anonymous

then the ? on the left is 51 and the ? on the right is 69

- anonymous

math student 55 am i right?

- mathstudent55

540 - 120 - 60 - 60 - 30 - 30 - 60 - 60 = 120
The sum of the measures of the missing angles is 120.

- anonymous

I don't understand how you would get ? though.

- mathstudent55

|dw:1437538419243:dw|

- mathstudent55

|dw:1437538472592:dw|

- mathstudent55

|dw:1437538502849:dw|

- anonymous

How did you get 69?

- mathstudent55

The inscribed angle

- anonymous

i see

- mathstudent55

|dw:1437538600159:dw|

- mathstudent55

|dw:1437538634138:dw|

- anonymous

Okay then. I see how you got it. Thanks for the help. :)

- mathstudent55

I assumed that O is the center of the circle. Is my assumption correct?

- anonymous

Yeah it is

- mathstudent55

ok

- mathstudent55

Then you don't need to use the angles of a pentagon like I did above.

- mathstudent55

You need to know that a central angle measures the same as its arc.
An inscribed angle measures half of its arc.

- mathstudent55

|dw:1437538880449:dw|

- anonymous

Oh i was kinda confused about why the inscribed measures half of its arc.

- mathstudent55

Here is how you solve this problem. It is very few steps.
1. Arcs DE and BA are 60 degrees like their central angles.
|dw:1437538961885:dw|

- mathstudent55

2. Arc CDE is 42 + 60 = 102 deg
m

- mathstudent55

3, Subtract 360 - 42 - 60 - 120 - 60 = 78 to find arc BC
If BC = 78, then arc ABC = 138
m

- mathstudent55

That's it.

- anonymous

Thanks @mathstudent55 :D Your the best! I understand it better now.

- mathstudent55

You're welcome.

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