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Question

FIGURE In the accompanying figure, segments AB and CD are parallel, the measure of angle D is twice that of angle B, and the measures of segments AD and CD are a and b respectively. Then the measure of AB is equal to

Accepted Answer

With reference to the diagram above, let E be the point on AB such that DE||BC. Let ABC=. We then have = AED = EDC since AB||CD, so ADE= ADC- BDC=2- = , which means AED is isosceles. Therefore, AB=AE+EB=a+b, hence our answer is a+b.