1. Problem: Find the measures of angles formed by secants and tangents intersecting outside the circle. 2. Given angles and arcs: PA = 138°, AQ = 50°, DB = 125°, EA = 86°. 3. Using the exterior angle theorem for two secants/tangents intersecting outside the circle, $$m\angle = \frac{1}{2}|\text{difference of intercepted arcs}|$$ 4. Calculations: 1. $m\angle BQC = \frac{1}{2}|PA - AQ| = \frac{1}{2}|138 - 50| = \frac{1}{2} \times 88 = 44^\circ$ 2. $m\angle EPD = \frac{1}{2}|DB - EA| = \frac{1}{2}|125 - 86| = \frac{1}{2} \times 39 = 19.5^\circ$ 5. To find $m\angle ED$, $m\angle CDE$, $m\angle CBE$, $m\angle AB$ we need more information or clarification since these seem to be arcs or not specified clearly with intercepted arcs. II. Problem: Find the measures of angles/arcs formed by chords/secants inside the circle. Given: - Arc $WX = 130^\circ$ - Arc $VZ = 62^\circ$ 6. Interior intersection angle theorem: $$m\angle = \frac{1}{2} (\text{sum of intercepted arcs})$$ 7. Calculations: - $m\angle WVZ = \frac{1}{2}(WX + VZ) = \frac{1}{2}(130 + 62) = 96^\circ$ - $m\angle WVX = m\angle WVZ = 96^\circ$ (assuming same intercepted arcs) - $m\angle WZY$, $m\angle XY$, $m\angle WZY$ need intercepted arc sums. Summary: Only certain angles given arcs were computable exactly from provided data. Final answers: 1. $m\angle BQC = 44^\circ$ 2. $m\angle EPD = 19.5^\circ$ 6. $m\angle WVZ = m\angle WVX = 96^\circ$