Question

The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is ${10}^{\circ }$, find the three angles.

Answer 1

Let one of the angles of a triangle be x. If angles are arranged in descending order, then the angles will be $x,(x-{10}^{\circ })$ and $(x-{20}^{\circ })$

We know that, the sum of all angles in a triangle is equal to ${180}^{\circ }$. So, $x+(x-{10}^{\circ })+(x-{20}^{\circ })={180}^{\circ }$
$\Rightarrow x+x+x-{30}^{\circ }={180}^{\circ }\Rightarrow 3x={180}^{\circ }+{30}^{\circ }\Rightarrow 3x={210}^{\circ }\Rightarrow x=\frac{{210}^{\circ }}{3}={70}^{\circ }$
Hence, angles will be ${70}^{\circ },{70}^{\circ }-{10}^{\circ }$ and ${70}^{\circ }-{20}^{\circ }$ i.e. ${70}^{\circ },{60}^{\circ }$ and ${50}^{\circ }$