Question

A. Find x. The figure is not drawn to scale.

b. Is the triangle equilateral, isosceles, or scalene? Explain

Answer 1

as you can see in the graph, the arcs of arcQP + arcPR + arcQR = 360°, since they take up the whole circle.

therefore then


`\bf (8x-10)~~+~~(6x)~~+~~(10x+10)=360\implies 24x=360 \\\\\\ x=\cfrac{360}{24}\implies x=15\\\\ -------------------------------\\\\ \overline{QP}=8(15)-10\implies 120-10\implies \boxed{110} \\\\\\ \overline{PR}=6(15)\implies \boxed{90} \\\\\\ \overline{QR}=10(15)+10\implies 150+10\implies \boxed{160}`

notice, all sides differ in length, thus the triangle is a scalene triangle.