The following figure shows a triangle ABC with exterior angles as x, y and z.
In the same figure, if y>x>z; arrange sides AB, BC and AC in descending order of their lengths. And hence answer is AB>BC>AC
A
True
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B
False
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Solution
The correct option is A True Given, y>x>z -- (1) Since, x,y,z are the exterior angles, they will be 180o−∠BAC;180o−∠ABC,180o−∠ACB respectively. -- (2) Hence, from 1,2
=>180o−∠ABC>180o−∠BAC>180o−∠ACB =>∠ABC<∠BAC<∠ACB This means, the sides opposite to the angles will also have the same relation. =>AC<BC<AB or AB>BC>AC