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

If arc SQ 84 and RPS 26 what is the measure of arc RS need answer asap thank you class=

Respuesta :

Banabanana
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°
calculista

Answer:

[tex]arc\ RS=136\°[/tex]

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=[tex]26\°[/tex] ------> external angle

so

m∠RPS=[tex]\frac{1}{2}(arc\ RS-arc\ SQ)[/tex]

we have

m∠RPS=[tex]26\°[/tex]

[tex]arc\ SQ=84\°[/tex]

substitute the values

[tex]26\°=\frac{1}{2}(arc\ RS-84\°)[/tex]

Solve for arc RS

[tex]52\°=(arc\ RS-84\°)[/tex]

[tex]arc\ RS=52\°+84\°=136\°[/tex]