Aboat travels 8 miles north from point a to point b. then it moves in the direction s 40º w and reaches point c. finally, it turns s 40º e and returns to point a. the total distance covered by the boat is miles.

The distance covered by boat is 18.44 miles.

Step-by-step explanation:

Use the given information to draw a figure.

           (Alternate interior angles)

    (Supplementary angles)

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

Since two angles are same, therefore ABC is isosceles triangle.

Use Law of Sine:

The perimeter of triangle ABC is

Therefore the distance covered by boat is 18.44 miles.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.