Question

An angle measures 105.6° more than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

Answer:-

Let the angle be x

• Other angle=x+105.6°

we know that

$\boxed{\sf Sum\;of\:Supplementary\:Angles=180°}$

$\\ \sf \longmapsto \: x+(x+105.6°)=180$

$\\ \sf \longmapsto \: x+x+105.6=180$

$\\ \sf \longmapsto \: 2x+105=180$

$\\ \sf \longmapsto \: 2x=180-105.6$

$\\ \sf \longmapsto \: 2x=74.4$

$\\ \sf \longmapsto \: x=\dfrac{74.4}{2}$

$\\ \sf \longmapsto \: x=37.2°$

$\\ \sf \longmapsto \: x+105.6=37.2+105.6=142.8°$

• Angles are 37.2° and 142.8°