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Please help! I'm really confused.



Angle A = 8x - 2, angle B = 2x - 8, and angle C = 94 - 4x. List the sides of triangle ABC in order from shortest to longest.


Options: (all are line segments)

o AC, AB, BC

o AC, BC, AB

o AB, AC, BC

o AC, BC, AB

Verified Answer :

Answer:

First option is correct.

Step-by-step explanation:

In triangle ABC, \(\angle A=8x-2\), \(\angle B=2x-8\) and \(\angle C=94-4x\).

According to angle sum property of a triangle, the sum of interior angles of a triangle is 180 degree.

\(\angle A+\angle B+\angle C=180^{\circ}\)

\(8x-2+2x-8+94-4x=180\)

\(6x+84=180\)

\(6x=96\)

Divide both sides by 6.

\(x=16\)

Therefore the value of x is 16. The measure of angles are

\(\angle A=8(16)-2=126\)

\(\angle B=2(16)-8=24\)

\(\angle C=94-4(16)=30\)

The opposite angle of shortest side is always smallest interior angle. Similarly the opposite angle of longest side is always largest interior angle.

\(\angle B<\angle C<\angle A\)

\(AC

Therefore option 1 is correct.

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