Question

A salesperson travels from city A to city B and then to city C. From city C, the salesperson travels directly back to city A

as shown in the diagram below. Write the lengths of the legs of the trip in order from least to greatest.
city

Answer 1

1) city C to city A

2) city A to city B

3) city B to city C

Explanation:

step 1

Find the value of x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

substitute the given values and solve for x

(2x-5)°+(x-1)°+(x+2)°=180°

Group terms

4x-4=180

4x=180+4

4x=184

x=46

step 2

Find the measure of each angle

A=(2x-5)°------> A=2(46)-5=87°

B=(x-1)° -------> B=46-1=45°

C=(x+2)° -----> C=46+2=48°

Let

a ------> travel from city B to city C

b -----> travel from city C to city A

c -----> travel from city A to city B

we know that

If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle

so

The greater angle is angle A, the side opposite the greater angle is the side a (travel from city B to city C)

The lesser angle is angle B, the side opposite the greater angle is the side b (travel from city C to city A)

therefore

The lengths of the legs of the trip in order from least to greatest is

1) city C to city A

2) city A to city B

3) city B to city C