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

Mathematics

1 answer:

Dovator [93]3 years ago

6 0

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.

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