Question

An angle measures 143.4° less than the measure of a supplementary angle. What is the measure of each angle?

Answer 1

Given :-

Measure of an angle = x

Measure of another angle = x - 143.4

Each angle is the supplement of the other angle .

Which means :-

$x + x - 143.4= 180$

$2x - 143.4 = 180$

$2x = 180 + 143.4$

$2x = 323.4$

$x = \frac{323.4}{2}$

$\color{hotpink}x = 161.7$

Then :-

Measure of the first angle :-

$\color{hotpink} = 161.7°$

Measure of the second angle :-

$= x - 143.4$

$= 16.7 - 143.4$

$\color{hotpink} = 18.3°$

As the sum of the measure of each angle adds up to 180° (161.7+18.3=180) , we can conclude that we have found out the correct value of each of the angles .

Therefore , the measure of the first angle is = 161.7° and the measure of it's supplementary angle is = 18.3° .