Question 1176989
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The answer to question  (c)  in the post by  @CPhill,  giving angle  VOL = 110°,  is  INCORRECT.


The correct answer to this question is  125°,   which complements the angle  VEL  of  55°  to  180°.


It is the same correct answer as  Edwin produced to this problem in his post.

<A HREF=https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1177016.html>https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1177016.html</A>



For any quadrilateral, &nbsp;inscribed in a circle, &nbsp;its opposite angles are supplementary:
they complement each other to &nbsp;180°.



This property of quadrilaterals inscribed into a circle is a standard geometric statement 
which students learn/study in a standard Geometry curriculum.



See, &nbsp;for example, &nbsp;my lesson


<A HREF=https://www.algebra.com/algebra/homework/word/geometry/The-property-of-the-angles-of-a-quadrilateral-inscribed-in-a-circle.lesson>A property of the angles of a quadrilateral inscribed in a circle</A>


https://www.algebra.com/algebra/homework/word/geometry/The-property-of-the-angles-of-a-quadrilateral-inscribed-in-a-circle.lesson>


in this site.