Question

If arc SQ = 84° and ∠RPS = 26°, what is the measure of arc RS? need answer asap thank you

Answer 1

The angle formed by the intersection of tangent and secant outside the circle equals half the difference of the intercepted arcs ⇒
(arc RS - arc SQ)/2 = ∠RPS
(arc RS - 84)/2 = 26
arc RS - 84 = 26 * 2
arc RS - 84 = 52
arc RS = 52 + 84
arc RS = 136°

Answer 2

`arc\ RS=136\°`

Explanation:

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

In this problem

m∠RPS=
`26\°` ------> external angle

so

m∠RPS=
`(1)/(2)(arc\ RS-arc\ SQ)`

we have

m∠RPS=
`26\°`

`arc\ SQ=84\°`

substitute the values

`26\°=(1)/(2)(arc\ RS-84\°)`

Solve for arc RS

`52\°=(arc\ RS-84\°)`

`arc\ RS=52\°+84\°=136\°`