Question

Can someone help please

Answer 1

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.

$m \angle PQS = \frac{1}{2}\times m(ar \ QTS)$

              $= \frac{1}{2}\times260^\circ$

              $=130^\circ$

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°.