Question

1. $mangle kml = \frac{1}{2} = left( moverarc{kl}

ight)$ 4. $diamondsuit$

1. $mangle kjl = mangle kml$ 5. $spadesuit$

$spadesuit$ =
$diamondsuit$ = angle formed by a tangent and a chord thm.
inscribed angle thm.
$spadesuit$ = second corollary to the inscribed angle thm.
substitution property

Explanation:

Step 1: Analyze \(m\angle KML=\frac{1}{2}(m\overarc{KL})\)

The formula \(m\angle KML=\frac{1}{2}(m\overarc{KL})\) is based on the inscribed - angle theorem. The inscribed - angle theorem states that an inscribed angle in a circle is half the measure of the arc it intercepts. Here, \(\angle KML\) is an inscribed angle that intercepts arc \(KL\).

Step 2: Analyze \(m\angle KJL = m\angle KML\)

Since \(\angle KJL\) and \(\angle KML\) are inscribed angles that intercept the same arc \(KL\). By the second corollary to the inscribed - angle theorem, inscribed angles that intercept the same arc are congruent.

Answer:

1. inscribed angle thm.
2. second corollary to the inscribed angle thm.