The measure of angle RQS is 50°.
Solution:
Given data:
m(ar QTS) = 260°
Tangent-chord theorem:
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.
[tex]$ m \angle PQS = \frac{1}{2}\times m(ar \ QTS)[/tex]
[tex]$ = \frac{1}{2}\times260^\circ[/tex]
[tex]=130^\circ[/tex]
m∠PQS = 130°
Sum of the adjacent angles in a straight line is 180°.
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°.
