Question

In the following figure: $AB$ is the largest side and $BC$ is the smallest side of triangle $ABC$. Which is the smallest angle ?

Answer 1

As $AB$ is largest side of $△ABC$

$\therefore \angle ACB$ ( opposite angle ) will be largest angle.

As $BC$ is the smallest side of $△ABC$

$\therefore \angle CAB$ is the smallest angle.

Now according to linear pairs.

$\angle X>\angle Z$

As $AC$ is neither smaller nor the largest its angle is less than $\angle X$ and more then angle $Z.$

Hence, $Z<Y<X$ hence, $\angle Z$ smaller than $\angle Y$ than $\angle X.$