5. Given $m\angle GC = 149^\circ$ and $m\angle LSC = 39^\circ$, with $OK$ tangent to circle $C$, to find $m\angle C$ we would use properties of tangents and angles subtended by chords, but this problem is not requested for solution here. 6. Given $KC = OC$, $OK = 56$, and $RC = 24$, find $OR$, $RS$, and $KS$. Step 1: Since $KC = OC$, triangle $KOC$ is isosceles with $KC = OC$. Step 2: Use the given lengths and any right triangles or circle properties involving points $O$, $R$, $K$, and $C$ (since $OK$ and $RC$ are given). Step 3: Assuming $OR$ and $RS$ are segments on the circle or related chords, use Pythagoras or segment addition. Detailed knowns and assumptions are limited; more context is needed for exact numeric evaluation. 7. Given $m\angle ONO = 238^\circ$, find $m\angle POO$ and $m\angle POR$. Step 1: Recognize that $m\angle ONO$ represents an angle involving points $O$ and $N$ possibly in the circle. Step 2: The sum of angles around a point is $360^\circ$. Step 3: Calculate $m\angle POO = 360^\circ - m\angle ONO = 360^\circ - 238^\circ = 122^\circ$. Step 4: $m\angle POR$ likely depends on other angles; more info is needed or given assumptions. 8. $PR$ is a diameter of circle $O$, and $m\angle WY = 55^\circ$. Find: a. $m\angle PW$ b. $m\angle RPW$ c. $m\angle PRW$ d. $m\angle WRE$ e. $m\angle WER$ Step 1: Since $PR$ is a diameter, angle subtended by $PR$ at the circumference is $90^\circ$ by Thales' theorem. Step 2: Use given $m\angle WY = 55^\circ$ and circle properties to find requested angles. Step 3: For each angle, apply circle theorems and properties of tangent or chords as needed. Due to lack of numeric labels for points $W$, $E$, and $R$, exact numeric answers can't be concluded here. Note: Problems 6, 7, and 8 involve geometry with circles and points; without full figure and more data, numeric answers are limited. Slug: circle_angles Subject: geometry Desmos: {"latex": "", "features": {"intercepts": false, "extrema": false}} q_count: 3