Question

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

Answer 1

First option is correct.

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<AB<BC`

Therefore option 1 is correct.