Question

The sum of two angles of a triangle is ${80}^o$ and their difference is ${20}^o$. Find the angles of the triangle.

Answer 1

Consider a $△ABC$,

then according to the given condition we have:

$\angle A+\angle B={80}^o$ and $\angle A-\angle B={20}^o$

$\Rightarrow 2\angle A={100}^o$

$\Rightarrow \angle A={50}^o$

$\Rightarrow \angle B={30}^o$

Using the sum of all the angles of the triangle is ${180}^o$

We have: $\angle A+\angle B+\angle C={180}^o$

$\Rightarrow {50}^o+{30}^o+\angle C={180}^o$

$\Rightarrow \angle C={100}^o$

Hence $\angle A={50}^o$, $\angle B={30}^o$ and $\angle C={100}^o$