Question

given: circle m with inscribed ∠kjl and congruent radii jm and ml. prove: (mangle mjl=\frac{1}{2}(mwidehat{kl})). what is the missing reason in step 8? statements: 1. circle m with inscribed ∠kjl and congruent radii jm and ml. 2. △jml is isosceles. 3. (mangle mjl = mangle mlj). 4. (mangle mjl + mangle mlj=2(mangle mjl)). 5. (mangle kml = mangle mjl + mangle mlj). reasons: 1. given. 2. isos. △s have two congruent sides. 3. base ∠s of isos. △are ≅ and have = measures. 4. substitution property. 5. measure of ext. ∠ equals sum of measures of

Explanation:

Step1: Recall circle - angle relationship concepts

In a circle, the measure of an inscribed - angle is half the measure of its intercepted arc. Also, properties of isosceles triangles are used in the proof. Given the steps so far, we are building up to the final proof of the inscribed - angle theorem.

Step2: Analyze the missing step

The step before the missing step shows that \(m\angle KML=m\angle MJL + m\angle MLJ\) and we know from step 4 that \(m\angle MJL + m\angle MLJ = 2(m\angle MJL)\). So, substituting \(m\angle MJL + m\angle MLJ\) with \(2(m\angle MJL)\) in the equation \(m\angle KML=m\angle MJL + m\angle MLJ\) gives us \(m\angle KML = 2(m\angle MJL)\), which can be rewritten as \(m\angle MJL=\frac{1}{2}(m\angle KML)\). The missing reason is the substitution property.

Answer:

substitution property