Drag an answer to each box to complete this paragraph proof. given: ∠pqr and ∠rqs are supplementary angles and m∠pqr=115° prove: ∠rqs is an acute angle. it is given that ∠pqr and ∠rqs are supplementary angles. so, m∠pqr+m∠rqs=180° using the . it is also given thatm∠pqr=115° . using the substitution property of equality, + m∠rqs=180° . using the subtraction property of equality, m∠pqr=65° . therefore, ∠rqs is an acute angle by . a. definition of complementary angles b. definition of supplementary angles c. definition of acute angle d. definition of obtuse angle e. 180° f. 115° image uploaded below: v v v

The correct options for blank 1,2 and 3 are B, F and C respectively.

Explanation:

It is given that the ∠PQR and ∠RQS are supplementary angles and ∠PQR=115°.

The two angles are called supplementary angles if they are  lies on the same arc of a straight line and their sum is 180 degree.

Since it is given that ∠PQR and ∠RQS are supplementary angles, so by the definition of supplementary angles we can say that their sum is 180 degree.

   .... (1)

Therefore, the correct option for first blank is option B.

It is given that ∠PQR=115°.

Using the substitution property of equality, the equation (1) can be written as,

Therefore, the correct option for second blank is option F.

Using the subtraction property of equality, ∠PQR=65° .

An angle less that 90 degree is called an acute angle and the an angle more than 90 degree but not more that 180 degree is called an obtuse angle.

Since 65 is less than 90, so by the definition of acute angle the ∠RQS is an acute angle.

Therefore, the correct option for third blank is option C.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)