The supplement of an angle is 12 less than 3 times the angle. Find the angle and its supplement

Question

asked Jan 19, 2022 190k views

1 Answer

Raja Fawad · Answer 1 · 2022-01-25T10:33:51+0000

Answer:

$\text{Angle: }48^(\circ),\\\text{Angle's supplement: }132^(\circ)$

Explanation:

Let the angle be
$\theta$ . Supplementary angles are angles that add up to
$180^(\circ)$ . Therefore, we can set up the following equation:

For some angle
$\theta$ , the supplement of
$\theta$ will be
$180-\theta$ .

$3\theta=(180-\theta)+12,\\3\theta -12=180-\theta,\\4\theta=192,\\\theta=(192)/(4)=\boxed{48^(\circ)}$

Now solving for the supplement:

$\text{Supplement}=180-\theta=180-48=\boxed{132^(\circ)}$