In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
diagram
quadrilateral inscribed in a circle
Step 02:
geometry:
quadrilateral and circle
we must analyze the graph to find the solution
the arc from E to C passing through D:
1/2 arc EC (passing through D) = ∠ B
arc EC (passing through D) = 2 * 100° = 200°
the arc from B to D passing through C:
1/2 arc BD (passing through C) = ∠ E
arc BD (passing through C) = 2 * 50° = 100°
angle BCD:
∠ BCD + ∠ BED = 180°
∠ BCD + 50° = 180°
∠ BCD = 180° - 50° = 130°
angle CDE:
∠ CDE + ∠ CBE = 180°
∠ CDE + 100° = 180°
∠ CDE = 180° - 100° = 80°
The answer is:
True statements:
2. The arc from B to D passing through C measures 100 degrees.
5. The sum of the measures of the arcs from E to C, one passing through D and the other passing through B, is 360 degrees.
6. Angle CDE measures 80 degrees.