Write the equation of each line in slope intercept form

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Ответ:

Nathaliasmiles

17.08.2022

Mathematics

b. 120°

Step-by-step explanation:

K is any point outside of the circle with center M.

KJ and KL are tangents to the circle at points J and L respectively drawn from point K.

MJ and ML are radii of the circle with center M.

Since, tangent is perpendicular to the radius of the circle.

$\therefore m\angle MJK = m\angle MLK = 90\degree \\$

Since, measure of central angle of a circle is equal to the measure of its corresponding minor arc.

$\therefore m\angle JML = m\widehat {(JL)} \\\therefore m\angle JML = 60\degree \\$

Since, JKLM is a quadrilateral. Hence by angle sum postulate of interior angles of quadrilateral JKLM, we have:

$m\angle JML + m\angle MJK + m\angle MLK \\+ m\angle JKL= 360\degree \\\therefore 60\degree +90\degree +90\degree +m\angle JKL= 360\degree \\\therefore 240\degree +m\angle JKL= 360\degree \\\therefore m\angle JKL= 360\degree-240\degree \\\huge \purple {\boxed {\therefore m\angle JKL= 120\degree}} \\$

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