Question

The angles of a triangle, in ascending order, are x, y, z and $y-x=z-y={10}^0$. 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 angle of triangle in ascending order are $x,y,z$

And $y-x=z-y=10$

Then $y-x=10\Rightarrow x=y-10$

And $z-y=10\Rightarrow z=y+10$

$x+y+z=180\Rightarrow y-10+y+y+10=180$

$\Rightarrow 3y=180$

$\Rightarrow y={60}^0$

Then $x=y-10=60-10={50}^0$

And $z=y+10=60+10={70}^0$

So the smallest angle is ${50}^0$