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  • ABCD is a trapezium in which AB || DC and A = B = 45º. Find angles C and D of the trapezium.

ABCD is a trapezium in which AB \parallel DC and \angle A = \angle B = 45^{\circ}. Find angles C and D of the trapezium.  

Answers (1)

Answer: \angle D=\angle C=135^{\circ}

Solution.

Given: AB\parallel DC and \angle A=\angle E=45^{\circ}

If AB\parallel CD and BC is transversal then sum of co-interior angles is 180^{\circ}
\therefore \angle B+\angle C=180^{\circ}
45^{\circ}+\angle C=180^{\circ}
\angle C=180^{\circ}-45^{\circ}
\angle C=135^{\circ}
Similarly
\angle A+\angle D=180^{\circ}
45^{\circ}+\angle D=180^{\circ}
\angle D=180^{\circ}-45^{\circ}
\angle D=135^{\circ}
Hence angles C and D are 135^{\circ}  each.

Posted by

infoexpert26

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