Question

HELP PLEASE I BEG OF U

Answer 1

Therefore,

`m\angle KLM\approx53\°`

Explanation:

Given:

KM = 8

r = 5

To Find:

m∠KLM = ?

Solution:

Chord length formula is given by

`\textrm{Chord length}=2r\sin ((\theta)/(2))`

where r is the radius of the circle and

'θ' is the angle from the center of the circle to the two points of the chord.

Let m∠KOM = θ be the center angle , Chord length = KM =8

So on Substituting the values we get

`8=2* 5\sin ((\theta)/(2))\\\\(\theta)/(2)=\sin^(-1)(0.8)=53.13\\\\\therefore \theta=106.26`

m∠KOM = θ = 106.3

Now by Inscribed angle theorem we have

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

Therefore

`m\angle KLM=(1)/(2)(m\angle KOM)`

Substituting the values we get

`m\angle KLM=(1)/(2)(106.3)`

Therefore,

`m\angle KLM\approx53\°`