Question

ABCD is a trapezium such that AB//CD, angle A: angle D=2:1, angle B: angle C=7:5. Find all the angles of trapezium.

Answer 1

ABCD is a trapezium....given

AB||CD...given

Let angle A=2x,B=7x,C=5x and D=x...from given and say

Therefore,AB||CD with transversal BC

Therefore angle ABC+angle DCB=180°...interior angles

i.e. angle C+angle B=180°

therefore 5x+7x=180°

12x=180°

x=15

therefore angle A=2x=2×15°=30,B=7x=7×15=105°,C=5x=5×15=75° and D=x=15°

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