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

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 $\angle R Q S = {290}^{\circ}$
then the situation is impossible. If $Q S$ is a diameter then for any point $R$ on the circumference, $\angle Q R S = {90}^{\circ}$; but combined with $\angle R Q S = {290}^{\circ}$ this implies that the interior angles of such a triangle exceed ${360}^{\circ}$

Jun 10, 2017

$m \angle R O S = {70}^{\circ}$
$m \angle R Q S = {290}^{\circ}$ means that the arc $\hat{R Q S}$ subtends an angle of ${290}^{\circ}$ at the centre.
As the complete circle is ${360}^{\circ}$
$\angle R O S$ is ${360}^{\circ} - {290}^{\circ} = {70}^{\circ}$