Question 1113624
here's a reference you should find useful.


<a href = "http://mathbitsnotebook.com/" target = "_blank">http://mathbitsnotebook.com/</a>


the particular section you would be interested in is:


<a href = "http://mathbitsnotebook.com/Geometry/Circles/CRAngles.html" target = "_blank">http://mathbitsnotebook.com/Geometry/Circles/CRAngles.html</a>


here's my completed picture of your diagram.


<img src = "http://theo.x10hosting.com/2018/040102.jpg" alt="$$$">


you can see from the diagram that angle C and angle B are both equal to 26 degrees.


this is because both are inscribed angles to arc ED which is equal to 52 degrees.


those angles are therefore 1/2 * 52 = 26 degrees.


you can also see from the diagram that angles E and angle D are each 57 degrees.


this is because both are inscribed angles to arc CB which is equal to 114 degrees.


1/2 * 114 = 57 degrees.


how did we get arc BC = 114 degrees?


angle D is 57 degrees and is an inscribed angle of arc BC.


this makes angle D equal to 1/2 the measure of arc BC.


you get 57 = 1/2 * BC.


solve for BC to get BC = 114 degrees.


angle BSD is equal to 97 degrees.


angle CSE is also equal to 97 degrees because it is a vertical angle to angle BSD.


why is angle BSD equal to 97 degrees/


because it is part of triangle BSD and the sum of the angle of a triangle is always equal to 180 degrees.


angles B and D total 83 degrees.


97 + 83 = 180 degrees.


angle BSD has to be equal to 97 degrees.


i think that answers all your questions.


you said:


I only need the measures angle C, angle B, angle BSD, angle CSE, angle E, the measure of Arc BC


angle C is equal to 26 degrees, angle B is equal to 26 degrees, angle BSD is equal to 97 degrees, angle CSE is equal to 97 degrees, angle E is equal to 57 degrees, the measure of arc BC is equal to 114 degrees.