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  • Write True or False and justify your answer in each of the following: ABCD is a cyclic quadrilateral such that \angle A = 90^{\circ}, \angle B = 70^{\circ}, \angle C = 95^{\circ} \; and \; \angle D = 105^{\circ}.

Write True or False and justify your answer in each of the following: ABCD is a cyclic quadrilateral such that \angle A = 90^{\circ}, \angle B = 70^{\circ}, \angle C = 95^{\circ} \; and \; \angle D = 105^{\circ}.

Answers (1)

False.

Solution:

In a cyclic Quadrilateral, the sum of opposite pairs of the angles in the given quadrilateral must be equal to 180°.

Here    \angle A + \angle C = 90 ^{\circ} + 95 ^{\circ} = 185 ^{\circ}

\angle B + \angle D = 70 ^{\circ} + 105 ^{\circ} = 175 ^{\circ}

Hence, it is not a cyclic Quadrilateral because the sum of the measures of opposite angles is not equal to 180°

Therefore the given statement is false.

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infoexpert24

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