Question

The angles of triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is $15$${}^o$, find the three angles.

Answer 1

Let one angle of the $△ABC$ be $x^o$.

Then the second angle $=(x+15{)}^o$, tThird angle$=(x+15+15{)}^o=(x+30{)}^o$

We know that sum of interior angles of a triangle is ${180}^o$

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

$\Rightarrow x+x+15+x+30=180$

$\Rightarrow 3x=180-45=135$

$\Rightarrow x=45$

$\therefore$ Angles are ${45}^o,{60}^o,{75}^o$