Question

Given: Circle M with inscribed Angle K J L and congruent radii JM and ML Prove: mAngle M J L = One-half (measure of arc K L) Circle M is shown. Line segment J K is a diameter. Line segment J L is a secant. A line is drawn from point L to point M. What is the missing reason in step 8?

Answer 1

Answer:

a) reflexive property

Step-by-step explanation:

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Answer 2

Answer:

We need to demontrate

$m \angle MJL = \frac{1}{2}arc(KL)$

As you can see in the figure below, angle MJL is an inscribed angle for Circle M, that means we can use the inscribed angle theorem to demonstrate the proposition above.

Therorem.

The angle formed by two intersecting chords with vertex on the circumference is equal to one-half of the intercepted arc.

Notice that the theorem says a chord. However, a diameter is a chord by definition, because a chord is a segment that unites to points of the circumference, and a diameter does that too.

Therefore, based on the inscribed angle arc theorem, we have

$m \angle MJL = \frac{1}{2}arc(KL)$