Question

The measure of an angle is eight times the measure of it’s supplementary angle.what is the measure of each angle?

Answer 1

Answer:

The measure of the supplementary angles are $160^{0}$ and $20^{0}$.

Step-by-step explanation:

Two angles, measuring less than or equal to $180^{0}$, are said to supplementary if their sum is $180^{0}$.

Let us suppose that the measure of one angle is $x^{0}$.

Then the measure of other angle is, $(180^{0} -x^{0})$.

It is provided that the measure of an angle is eight times the measure of it’s supplementary angle, that is

$x^{0} =8(180^{0} -x^{0})$

Solving this equation for $x^{0}$,

$x^{0} =8(180^{0} -x^{0})\\x^{0} =1440^{0} -8x^{0}\\9x^{0}=1440\\x^{0}=160^{0}$

So the measure of one angle is $160^{0}$.

Then the measure of the other angle is,

$180^{0} -x^{0} = 180^{0} -160^{0} \\=20^{0}$

Therefore, the measure of the supplementary angles are $160^{0}$ and $20^{0}$.