Question

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

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

Answer 1

The correct option is C ${50}^{\circ }$

Given, $y-x=z-y=10$

We know, $x+y+z=180$ .........Sum of all angles of triangle is equal to ${180}^o$
Therefore, $x+(x+10)+(x+10+10)=180$
$\Rightarrow 3x=150$
$\Rightarrow x={50}^o$

So, option C is correct.