Question

The angles of a triangle are arranged in ascending order of their magnitude. If the difference between two consecutive angles is ${10}^o$, find the three angles.

Answer 1

Let one angle of a triangle be $x$.

Second angle will be $x+10$.

Third angle will be $x+20$.

Using theorem, Sum of interior angles of a triangle is ${180}^o$ .

Hence $\angle A+\angle B+\angle C={180}^o$

$\Rightarrow x+x+10+x+20={180}^o$

$\Rightarrow 3x+30={180}^o$

$\Rightarrow x={50}^o$

$\therefore$ Angles are ${50}^o,{60}^o,{70}^o.$