Picture: http://postimg.org/image/kad9sveer/
In the figure, SP and RQ are produced to meet at T. If ∠QPS=101° and PTRO is a cyclic quadrilateral, find ∠RST and ∠STR.
How can I find ∠RST? Using similar triangle, joining lines or other methods?
Thank you!
F.5 Maths circle
2014-11-19 1:10 am
回答 (2)
2014-11-19 2:26 am
✔ 最佳答案
Let angle RST = xso angle ROP = 2x (angle at centre)
so angle STR = 180 - 2x (PTRO is a cyclic quad.)
Angle PQT = angle RST = x (ext. angle of cyclic quad.)
Angle STR + angle PQT = angle QPS = 101 (ext. angle of triangle)
that is
(180 - 2x) + x = 101
x = 180 - 101 = 79 degree = angle RST
angle STR = 180 - 2x = 180 - 2(79) = 180 - 158 = 22 degree.
2014-11-19 3:05 am
收錄日期: 2021-04-15 17:15:31
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https://hk.answers.yahoo.com/question/index?qid=20141118000051KK00048