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Need help how would I find which ones are true for this quadrilateral inscribed in a circle?

Need help how would I find which ones are true for this quadrilateral inscribed in-example-1
Need help how would I find which ones are true for this quadrilateral inscribed in-example-1
Need help how would I find which ones are true for this quadrilateral inscribed in-example-2
User Hshan
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1 Answer

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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.

User Andrew Shelansky
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