Question 1144649: AB is a diameter of a semicircle of cyclic quadilateral ABCD. If A =62degree, calculate B,C and D. (show working)
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
The formulation of the problem in your post is . . . m-m-m, how to say it . . . absolutely unprofessional.
The proper formulation is this :
In a cyclic quadrilateral ABCD, the side AB is the diameter of the circle. If A = 62 degrees, find angle C.
Solution
Use the Theorem
If a convex quadrilateral is inscribed in a circle, then the sum of its opposite angles is equal to 180°.
From this theorem, you momentarily get for the angle C, which is opposite to angle A
m (C) = 180° - m(A) = 180° - 62° = 118°. ANSWER
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Regarding this theorem, see the lesson
- Quadrilateral inscribed in a circle
in this site.
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And you can not determine NEITHER angle B nor D based on given condition.
You know only that m(B) + m(D) = 180° , and nothing more.
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You should say / post your "THANKS" at least three times to me:
- first time for explaining to you on how to formulate your problem properly;
- second time for solving the problem for you;
- and third time for referring you to this excellent lesson.
So, I really expect to get this triple "THANKS".
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Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part of this online textbook under the topic "Properties of polygons".
Also, you can find practically every topic of the school Geometry presented in perfect logical form.
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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