Question

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

Answer 1

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^@`
then the situation is impossible. If `QS` is a diameter then for any point `R` on the circumference, `/_QRS = 90^@`; but combined with `/_RQS=290^@` this implies that the interior angles of such a triangle exceed `360^@`

Answer 2

`m/_ROS=70^@`

Explanation:

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

As the complete circle is `360^@`

`/_ROS` is `360^@-290^@=70^@`