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In trapezium ABCD, AB is parallel to CD. Given that angle ADC = 2 * angle ABC, with AD = a cm and CD = b cm, find the length of AB in cm.

1. a/2 + 2b
2. a + b
3. (2/3)*a + b
4. a + (2/3)*b

Correct answer: a + b

Solution

Because AB || CD, co-interior and alternate angle relations combine with angle ADC = 2*angle ABC to make a sub-triangle isosceles, so AB splits into a segment equal to CD (b) plus a segment equal to AD (a).

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