Question

The measure of the supplement of an angle is 84° less than the measure of the angle. Find the measures of the angles

Answer 1

Let the measure of angle be 'x'

Since, the measure of the supplement of an angle is 84° less than the measure of the angle.

Therefore, measure of supplement of x = x - 84°

The measure of two supplementary angles is 180 degrees.

$x + x -84^\circ = 180^\circ$

$2x -84^\circ = 180^\circ$

$2x =84^\circ + 180^\circ$

$2x =264^\circ$

$x =132^\circ$

So, the measure of angle =$x =132^\circ$

Its supplement = x - 84°  = 132°  - 84°

=  48°

So, the measure of supplement of angle is 48 degrees.