Question

What is the measure of RST ?
A. 94
B. 210
C. 170
D. 190

Answer 1

The measure of arc RST is 170

Option C is correct.

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)

`m\angle RTS=(1)/(2)* m(arc RS)=(1)/(2)* 94=47^(\circ)`

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.

Answer 2

The measure of arc ST is twice that of ∠Q, so is 96°. Then the measure of arc RST is 94° +96° = 190°.

The appropriate choice is
D. 190