Question

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Answer 1

Given:

A figure of a circle and two secants on the circle from the outside of the circle.

To find:

The measure of angle KLM.

Solution:

According to the intersecting secant theorem, if two secant of a circle intersect each other outside the circle, then the angle formed on the intersection is half of the difference between the intercepted arcs.

Using intersecting secant theorem, we get

`\angle KLM=(1)/(2)(Arc(JON)-Arc(KM))`

`(3x-4)=(1)/(2)(271-(x+6))`

`(3x-4)=(1)/(2)(271-x-6)`

Multiply both sides by 2.

`6x-8=265-x`

Isolate the variable x.

`6x+x=265+8`

`7x=273`

Divide both sides by 7.

`x=(273)/(7)`

`x=39`

Now,

`\angle KLM=(3x-4)^\circ`

`\angle KLM=(3(39)-4)^\circ`

`\angle KLM=(117-4)^\circ`

`\angle KLM=113^\circ`

Therefore, the measure of angle KLM is 113 degrees.