Question

The sum of two angles is ${123}^{\circ }$ and their difference is ${13}^{\circ }.$ Find all the angles of the triangle.

Answer 1

Let two angles are $x$ and $y$, then according to question
$\angle x+\angle y={123}^{\circ }\dots$(i)
and $\angle x-\angle y={13}^{\circ }\dots$(ii)
Adding (i) and (ii), we get
$2\angle x={136}^{\circ }\Rightarrow \angle x={68}^{\circ }$
Now substituting $\angle x={68}^{\circ }$ in equation (i), we get
${68}^{\circ }+\angle y={123}^{\circ }$
$\Rightarrow \angle y={123}^{\circ }-{68}^{\circ }={55}^{\circ }$
Third angle $={180}^o-(\angle x+\angle y)={180}^{\circ }-{123}^{\circ }={57}^{\circ }$
Hence angles of a triangle are ${68}^{\circ },{55}^{\circ },{57}^{\circ }$