Question

What’s the correct answer for this?

Answer 1

`\fbox{\begin{minipage}{8.8em}Option D is correct\end{minipage}}`

Step-by-step explanation:

Here, we state again the definition of inscribed angle in circle:

(1) An inscribed angle has the vertex on the circle and the sides are chords.

=> In the picture shown, angle ELK is inscribed angle with vertex L and LE and LK are chords.

(2)An inscribed angle also creates an intercepted arc whose endpoints are on the angle.

=> Inscribed angle ELK creates intercepted arc EK.

(3) According to the Inscribed Angle Theorem, the measure of intercepted arc is twice as the measure of its inscribed angle.

=> Angle ELK = (1/2) arc EK

Arc EK, whose EK is diameter, is equal to measure of half of circle, or 180 degree, in other words.

=> Angle ELK = (1/2) x 180 = 90 deg

(4) As the property of sum of 3 angles inside a triangle, this sum is equal to 180 degree.

=> Considering triangle ELK:

ELK + LEK + LKE = 180 deg

or

90 + 55 + LKE = 180 deg

or

LKE = 180 - 90 - 55 = 35 deg

Hope this helps!

:)

Answer 2

D: <K = 35°

Step-by-step explanation:

<E = 55

<L = 90°

Now

<LKE = 180-90-55

<K = 35°