Answer:
51°
Step-by-step explanation:
An inscribed angle is half of the arc it intercepts. This means that arc QR is twice m<QTR or 78°.
Since <QSR is a central angle, it equals the arc it intercepts. This means m<QSR equals arc QR which is 78°.
We can say that QS equals to RS because they are both radii, and radii of the same circle are equal. This means triangle QSR is isosceles.
Let <QRS equal x. Because of base angle theorem, <SQR would also be equal to x. Since the angles in a triangle add up to 180, we can write an equation to model the situation:
m<QRS + m<SQR + m<QSR = 180
We can substitute the values we have:
x + x + 78 = 180
2x = 102
x = 51
Since <QRS is equal to x, it is 51°
