Which statement about bq←→ is correct?

bq←→ is a tangent line because m∠abq=90°.

bq←→ is a tangent line because △abq is not a right triangle.

bq←→ is not a tangent line because ∠baq is an acute angle.

bq←→ is not a tangent line because ∠bqa is an acute angle.

We have a circle A and a line segment BQ is passing through the circle A such that it forms a triangle ABQ.

From the diagram, we have some information about the angles of triangle ΔABQ as follows :-

angle QAB = 36 degrees and angle BAQ = 54 degrees.

We know about the Triangle Sum theorem which states "The sum of all interior angles of any triangle is 180 degrees".

We can use this theorem to find the third angle of the triangle ΔABQ.

∠ABQ + ∠BQA + ∠QAB = 180 degrees

∠ABQ + 54° + 36° = 180°

∠ABQ + 90° = 180°

∠ABQ = 180° - 90°

∠ABQ = 90 degrees

If any line makes a right angle with the radius of any circle, then this line must be a tangent to that circle.

So, BQ would be a tangent line because angle ∠ABQ = 90 degrees. Hence, option A is correct.

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.