Question

6. m A = 8x - 2, m B = 2x - 8, and m2 C = 94 - 4x. List the sides of A ABC in order from shortest to

Answer 1

Given:

In triangle ABC, m∠A=(8x-2)°, m∠B=(2x-8)° and m∠C=(94-4x)°.

To find:

The sides of the triangle ABC in order from shortest to  longest.

Solution:

In triangle ABC,

$m\angle A+m\angle B+m\angle C=180^\circ$              (Angle sum property)

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

$(6x+84)^\circ=180^\circ$

$6x+84=180$

$6x=180-84$

$6x=96$

Divide both sides by 6.

$x=\dfrac{96}{6}$

$x=16$

Now,

$m\angle A=(8(16)-2)^\circ$

$m\angle A=(128-2)^\circ$

$m\angle A=126^\circ$

Similarly,

$m\angle B=(2(16)-8)^\circ$

$m\angle B=(32-8)^\circ$

$m\angle B=24^\circ$

And,

$m\angle C=(94-4(16))^\circ$

$m\angle C=(94-64)^\circ$

$m\angle C=30^\circ$

In a triangle the smaller angle has shorter opposite side and larger angle has longer opposite side.

$24^\circ$

$m\angle B$

$AC$

List the sides of triangle ABC in order from shortest to  longest is AC:AB:BC.

Therefore, the correct option is A.