In Fig.10.15, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of \angleACD + \angleBED.

Answers (1)

270°

Solution:

Join AE

ACDE is a cyclic quadrilateral and sum of opposite angles in a cyclic quadrilateral is 180°

\therefore \angleACD + \angleAED = 180°                  … (i)

Now, we know that the angle in a semi-circle is 90°

So, \angleAEB = 90°                                 … (ii)

An adding equation (i) & (ii), we get.

\angleACD + \angleAED + \angleAEB = 180° + 90°

\angleACD + \angleBED = 270°

Hence the value of \angleACD + \angleBED is 270°

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