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Blababa [14]
3 years ago
5

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

Mathematics
2 answers:
weeeeeb [17]3 years ago
5 0
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 = <span>∠RPS
(</span>arc RS - 84)/2 = 26
arc RS - 84 = 26 * 2
arc RS - 84 = 52
arc RS = 52 + 84
arc RS = 136°
Lera25 [3.4K]3 years ago
3 0

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\°

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