Question

State true or false:

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
• B. False

Answer 1

The correct option is A True

Given, $y>x>z$ -- (1)
Since, $x,y,z$ are the exterior angles, they will be ${180}^o-\angle BAC;{180}^o-\angle ABC,{180}^o-\angle ACB$ respectively. -- (2)
Hence, from $1,2$

$=>{180}^o-\angle ABC>{180}^o-\angle BAC>{180}^o-\angle ACB$
$=>\angle ABC<\angle BAC<\angle ACB$
This means, the sides opposite to the angles will also have the same relation.
$=>AC<BC<AB$ or $AB>BC>AC$