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Sphinxa [80]
3 years ago
11

I need help please helppppppppppppppppppppppp

Mathematics
1 answer:
Marrrta [24]3 years ago
5 0

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=\dfrac{1}{2}(Arc(JON)-Arc(KM))

(3x-4)=\dfrac{1}{2}(271-(x+6))

(3x-4)=\dfrac{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=\dfrac{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.

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