Answer:
The measure of arc RST is 170
Option C is correct.
Step-by-step explanation:
Given the figure in which measure of ∠TQS=48° and measure of arc RS=94°
we have to find the measure of arc RST.
By the theorem, the angles in the same segment are equal, i.e. angles subtended by the same arc at the circumference are equal.
∴ ∠TQS=∠TRS=48°
Also the angle which is subtended at the centre of a circle is twice the angle subtended at any point on the circumference i.e
m(arc RS)=2(m∠RTS)
[tex]m\angle RTS=\frac{1}{2}\times m(arc RS)=\frac{1}{2}\times 94=47^{\circ}[/tex]
In ΔRTS, by angle sum property of triangle
∠RTS+∠RST+∠TRS=180°
47°+∠RST+48°=180°
∠RST+95°=180°
∠RST=85°
∴ The measure of arc RST is twice the angle ∠RST
m(arc RST)=2(85)=170
Hence, option C is correct.
