SOLUTION: Find x. circle with points A, B, C, and D on the circle, segments AC and BD crossing at point E inside the circle, arc BC is 65 degrees, arc AD is 80 degrees and angle BEC is x

Algebra ->  Triangles -> SOLUTION: Find x. circle with points A, B, C, and D on the circle, segments AC and BD crossing at point E inside the circle, arc BC is 65 degrees, arc AD is 80 degrees and angle BEC is x      Log On


   



Question 1083233: Find x.
circle with points A, B, C, and D on the circle, segments AC and BD crossing at point E inside the circle, arc BC is 65 degrees, arc AD is 80 degrees and angle BEC is x degrees

Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  Make a sketch.


2.  Use the Theorem:

        The angle between two chords intersecting inside a circle has the measure half the sum of the measures the arcs intercepted by the chords. 


3.  It gives the measure of the angle BEC = %281%2F2%29%2A%2865%5Eo%2B80%5Eo%29 = 72.5 degs.

See the lesson
    - The angle between two chords intersecting inside a circle
in this site.

Also,  you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part if this textbook under the topic
"Properties of circles, inscribed angles, chords, secants and tangents".