Question

in figure O is the centre of the circle and angle BOC is equal to 120 degree find angle C D E

Answer 1

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Answer 2

Answer:

The measure of angle CDE is 60°.

Step-by-step explanation:

Given information:

$\angle BOC=120^{\circ}$

Using central angle theorem,

$\angle BOC=2\angle BAC$

$120=2\angle BAC$

$\angle BAC=60^{\circ}$

The measure of angle BAC is 60 degrees.

ABCD is a cyclic quadrilateral. So the sum of opposite angles is 180.

$\angle BDC+\angle BAC=180$

$\angle BDC+60=180$

$\angle BDC=120$

The measure of angle BDC is 120 degrees.

Angle BDC and CDE are lie on a starlight line, so both angles are supplementary angles and their sum is 180 degree.

$\angle BDC+\angle CDE=180$

$120+\angle CDE=180$

$\angle CDE=60^{\circ}$

Therefore the measure of angle CDE is 60°.