Question

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

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

Answer 1

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

Consider the given equation.

$y-x={10}^0$ $..........\left(1\right)$

$z-y={10}^0$ $...........\left(2\right)$

We know that

$x+y+z={180}^0$ $...........\left(3\right)$

On solving all equations, we get

$x={50}^0,y={60}^0,z={70}^0$

Hence, the smallest angle is ${50}^0$.