Quadrilateral bcde is inscribed inside a circle as shown below. write a proof showing that angles c and e are supplementary. circle a is shown with an inscribed quadrilateral labeled bcde.

The sum of angle C and E is 180°. So, C and E are supplementary angles.

Step-by-step explanation:

Given information: Quadrilateral BCDE is inscribed inside a circle.

To prove : angles C and E are supplementary, i.e., ∠C+∠E=180°.

Proof:

BCDE is a cyclic quadrilateral.

According to central angles theorem, the inscribed angle on a circle is half of its central angle.

By using Central angle theorem

                .... (1)

             ..... (2)

The complete central angles of a circle is 360°.

Using (1) and (2), we get

Divide both sides by 2.

The sum of angle C and E is 180°. So, C and E are supplementary angles.

Hence proved.

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step-by-step explanation: hope i you and who ever sees this answer have a great rest of your day : )

answer is 67%

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