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

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.

$\angle B<\angle C<\angle A$

$AC<AB<BC$

Therefore option 1 is correct.