Question

HELP!!! all work is due in 2 hours

Answer 1

The outside arcs for a circle enveloping a triangle will always equal 360.

Set up an equation that has all arcs equal 360:

$(3x + 30) + (5x + 10) + (2x + 20) = 360$

Combine like terms:

$3x + 5x + 2x = 10x$
$30 + 10 + 20 = 60$

$10x + 60 = 360$

Subtract 60 from both sides:

$10x = 300$

Divide both sides by 10 to get x by itself:

$x = 30$

We can now find the values of the arcs:

$3(30) + 30 = 90 + 30 = 120$
$5(30) + 10 = 150 + 10 = 160$
$2(30) + 20 = 60 + 20 = 80$

All three arc lengths are different, which means that the triangle's side lengths are all different. This makes the triangle a scalene triangle.