Answer:
a. x = 15
b. scalene
Step-by-step explanation:
You want to know the value of x and the classification of the triangle whose circumscribing arcs are (8x-10)°, (6x)°, and (10x +10)°.
a. Arcs
The sum of arcs around the circle is 360°.
(8x -10)° +(6x)° +(10x +10)° = 360°
24x = 360 . . . . . . . . . . . divide by °, simplify
x = 15 . . . . . . . . . . . . divide by 24
b. Triangle
The arc measures around the circle are ...
(8x -10)° = 110°
(6x)° = 90°
(10x +10)° = 160°
Each arc is double the measure of the inscribed angle that intercepts it. The different arc measures mean the angle measures are different, so the triangle is scalene.
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