K, L, and M are points on the circle. KS is a tangent to the circle at K. KM is a diameter and triangle KLM is isosceles. Find t

Question

1 year ago

10

he value of z.

1 answer:

Paraphin [41] · Answer 1 · 2023-05-06T16:21:50+03:00

Using the circle theorems, the value of z is 45

<h3>Circle Geometry </h3>

From the question, we are to determine the value of z

From the given information,

KM is a diameter

∴ ∠KLM = 90° (<em>Angle in a semicircle</em>)

Also, ΔKLM is isosceles

∴ ∠KML = ∠MKL (<em>Base angles of an isosceles triangle</em>)

Then,

∠KML + ∠MKL + ∠KLM = 180° (<em>Sum of angles in a triangle</em>)

2× ∠KML + 90° = 180°

2× ∠KML = 180° - 90°

2× ∠KML = 90°

∠KML = 90°/2

∠KML = 45°

Now, we can observe that

z° = ∠KML (<em>Angles in alternate segment</em>)

But,

∠KML = 45°

∴ z = 45

Hence, the value of z is 45

Learn more on Circle Geometry here: brainly.com/question/17074363

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