#1**+1 **

The sum of the arcs = 360° .... so we have

[8x - 10 ] + [ 10x + 10] + [6x] = 360 simplify

24x = 360 divide both sides by 24

x = 15

Note that the greatest angle in the triangle will be opposite the greatest arc, i.e., the arc denoted as

10x + 10

So.....the measure of this arc is 10(15) + 10 = 150 + 10 = 160°

But the angle opposite is an inscribed angle which will measure (1/2) of this arc = 80°

So since none of the arcs are equal.......this triangle is scalene [we could have probably seen this right away since we have no equal arcs and minor arc QR appears to be < 180°......thus angle QPR < 90° ]

CPhill
Apr 11, 2017