Points P, Q, and S are collinear. If ray QT bisects angle RQS, what is m angle TQS?

The angle TQS has a value of 23.5º.

Step-by-step explanation:

and are supplementary to each other, that is, the sum of angles equals 180º, and ray divides into two equal parts. We construct this system of linear equations after a careful reading of statement:

(Eq. 1)

(Eq. 2)

(Eq. 3)

(Eq. 4)

(Eq. 5)

Now we proceed to solve the system algebraically:

(Eq. 1) and (Eq. 2) in (Eq. 3)

In (Eq. 1):

(Eq. 5) in (Eq. 4):

The angle TQS has a value of 23.5º.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.