In the following figure; $A B$ is the largest side and $B C$ is the smallest side of triangle $A B C$ . Write the angles $x^{0}$ , $y^{0}$ and $z^{0}$ in ascending order of their values.

y^{0} < z^{0} < x^{0}

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z^{0} < y^{0} < x^{0}

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z^{0} > y^{0} > x^{0}

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z^{0} > x^{0} > y^{0}

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Solution

The correct option is B $z^{0} < y^{0} < x^{0}$
Given, sides $A B > A C > B C$
This means, the angles opposite to the sides will also have the same relation.
$=> ∠ A C B > ∠ A B C > ∠ B A C$ -- (1)
Since, $x^{o}, y^{o}, z^{o}$ are the exterior angles, they will be $180^{o} - ∠ B A C; 180^{o} - ∠ A B C, 180^{o} - ∠ A C B$ respectively. -- (2)
Hence, from $1, 2$
$=> 180^{o} - z^{o} > 180^{o} - y^{o} > 180^{o} - x^{o}$
$=> z^{o} < y^{o} < x^{o}$

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