Question

If arc SQ = 84° and ∠RPS = 26°, what is the measure of arc RS?

Answer 1

got pic?    anyway, is is 180-84-26 which is 96-26 so rs=70 degrees i think

Answer 2

`arc\ RS=136\°`

Explanation:

see the attached figure to better understand the problem

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\°`