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

Answer:

$arc\ RS=136\°$

Step-by-step 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=$\frac{1}{2}(arc\ RS-arc\ SQ)$

we have

m∠RPS=$26\°$

$arc\ SQ=84\°$

substitute the values

$26\°=\frac{1}{2}(arc\ RS-84\°)$

Solve for arc RS

$52\°=(arc\ RS-84\°)$

$arc\ RS=52\°+84\°=136\°$