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It is 60 and 60
My textbook says that angle ABC=111 and angle CDE=129
That is the answer but how do i get it?
ABCDE is a pentagon.
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
then the ? on the left is 51 and the ? on the right is 69
math student 55 am i right?
540 - 120 - 60 - 60 - 30 - 30 - 60 - 60 = 120 The sum of the measures of the missing angles is 120.
I don't understand how you would get ? though.
How did you get 69?
The inscribed angle
Okay then. I see how you got it. Thanks for the help. :)
I assumed that O is the center of the circle. Is my assumption correct?
Yeah it is
Then you don't need to use the angles of a pentagon like I did above.
You need to know that a central angle measures the same as its arc. An inscribed angle measures half of its arc.
Oh i was kinda confused about why the inscribed measures half of its arc.
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|
2. Arc CDE is 42 + 60 = 102 deg m
3, Subtract 360 - 42 - 60 - 120 - 60 = 78 to find arc BC If BC = 78, then arc ABC = 138 m
Thanks @mathstudent55 :D Your the best! I understand it better now.