arc RT = 49°
What is tangent?
"It is a line that intersects the circle exactly at one point."
What is secant?
"It is a line that intersects circle at two points."
For given example,
arc QT = (27x + 3)°
arc RT = (9x – 5)°
∠RST = (10x – 2)°
From figure we can observe that line ST is tangent and line SQ is secant.
∠RST is the angle subtended by tangent ST and secant SQ
We know, the angle subtended by the tangent and the secant is half the difference of the measures of the intercepted arcs.
⇒ ∠RST = (QT - RT)/2
⇒ 10x - 2 = [(27x + 3) - (9x - 5)] /2
⇒ 2(10x - 2) = 27x + 3 - 9x + 5
⇒ 20x - 4 = 18x + 8
⇒ 20x - 18x = 8 + 4
⇒ x = 6
So, arc RT would be,
⇒ 9x - 5 = 9(6) - 5
⇒ 9x - 5 = 49°
Therefore, arc RT = 49°
Learn more about tangent and secant here:
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