This figure shows circle O with diameter QS . mRQS=290∘ What is the measure of ∠ROS ?

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2 Answers
Jun 9, 2017

The situation described seems to be impossible.

Explanation:

The ambiguity in my response is based on the 4 non-displayable characters following "mRQS".

If I ignore these characters so the question claims /_RQS=290^@RQS=290
then the situation is impossible. If QSQS is a diameter then for any point RR on the circumference, /_QRS = 90^@QRS=90; but combined with /_RQS=290^@RQS=290 this implies that the interior angles of such a triangle exceed 360^@360

Jun 10, 2017

m/_ROS=70^@mROS=70

Explanation:

m/_RQS=290^@mRQS=290 means that the arc hat(RQS)ˆRQS subtends an angle of 290^@290 at the centre.

As the complete circle is 360^@360

/_ROSROS is 360^@-290^@=70^@360290=70