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The measure of angle RQS is 50°.
Solution:
Given data:
m(ar QTS) = 260°
<u>Tangent-chord theorem:</u>
<em>If a tangent and chord intersect at a point, then the measure of each angle formed is half of the measure of its intercepted arc.</em>
m∠PQS = 130°
<em>Sum of the adjacent angles in a straight line is 180°.</em>
m∠PQS + m∠RQS = 180°
130° + m∠RQS = 180°
Subtract 130° from both sides.
130° + m∠RQS - 130° = 180° - 130°
m∠RQS = 50°
The measure of angle RQS is 50°.