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NotSoSmart  Apr 11, 2017
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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° ]

 

 

cool cool cool

CPhill  Apr 11, 2017

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