The measure of the arc depends on the outside angle formed by the two
tangents, such that the given equations can be equated to find x.
Response:
The given parameters are;
m∠JKL = 8·x - 6
[tex]m\widehat{JML}[/tex] = 25·x - 13
We have that the external angle formed by two tangents, ∠JKL , is given
by the far arc, near arc theorem or the secant, tangent outside angle
theorem as follows, as follows;
[tex]\widehat{JML} - \widehat{JL}[/tex] = 2 × [tex]\mathbf{\angle {JKL}}[/tex]
[tex]\widehat{JML} + \widehat{JL}[/tex] = 360°
[tex]\widehat{JML} - \widehat{JL}[/tex] + [tex]\widehat{JML} + \widehat{JL}[/tex] = 2 × [tex]\mathbf{\widehat{JML}}[/tex]
[tex]\widehat{JML} - \widehat{JL}[/tex] + [tex]\widehat{JML} + \widehat{JL}[/tex] = 2 × [tex]\angle {JKL}[/tex] + 360°
Which gives;
2 × [tex]\angle {JKL}[/tex] + 360° = 2 × [tex]\widehat{JML}[/tex]
2 × (8·x - 6) + 360° = 2 × (25·x - 13)
2 × (8·x - 6) + 360° - 2 × (25·x - 13) = 0
-34·x + 374° = 0
374° = 34·x
[tex]x = \dfrac{374}{34} = 11[/tex]
[tex]m\widehat{JML}[/tex] = 25 × 11 - 13 = 262
Learn more about the intersecting secants outside angle theorem here:
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