Question

The angles of a triangle, in ascending order are $x,y$ and $z$ and $y-x=z-y={10}^o$. The smallest angle is:

• A. ${40}^o$
• B. ${60}^o$
• C. ${50}^o$
• D. ${70}^o$

Answer 1

The correct option is C ${50}^o$

Given, $y-x=z-y={10}^o$

$\Rightarrow y-x={10}^o,z-y={10}^o$

$\Rightarrow x=y-{10}^o,z={10}^o+y$ ....(1)

since, $x+y+z={180}^o$ $\left[\text{Angle sum property}\right]$

$y-{10}^o+y+{10}^o+y={180}^o$

$\Rightarrow 3y={180}^o\Rightarrow y={60}^o$

On substituting $y={60}^o$ in (1). we get,

$x={50}^o,z={70}^o$

$\therefore$ Smallest angle$={50}^o$

Option $C$ is correct.