To win a local billiards tournament, all Jeanette has left to do is drop the 9-ball. Because of the other balls on the table (not shown), her only realistic shot on this turn is to bounce the ball off both sides of the table as shown. Use the information in the image to answer the questions below. Lines AB and CH are parallel, and the near side of the table is parallel to the far side.

a. What other angle measures can we be sure about? Explain your reasoning.
b. Identify the sets of congruent angles. Explain your conclusions.
c. Identify all the sets of alternate interior angles you can envision. Explain.
d. Identify all the sets of corresponding angles. Explain.

Here's what I get.

Step-by-step explanation:

Assume the diagram is like the one below.

Segments AB, BC, and CH are transversals to the sides of the pool table.

BC is also a transversal to AB and CH.

a. Angles we can be sure about

∠ABC — interior opposite angles of transversal BC

∠CBH — interior opposite angles of transversal BC

∠BHC — interior angles of triangle BHC

∠ABK — alternate exterior angles of transversal BC

∠CHG — complementary to ∠CGH

b. Sets of congruent angles

∠ABC ≅ ∠BCH = 66° — interior opposite angles of transversal BC

∠CBH ≅ ∠BCE = 57° — interior opposite angles of transversal BC

∠BHC ≅ ∠GCH = 57° — interior opposite angles of transversal CH

∠ABK ≅ ∠GCH = 57° — alternate exterior angles of transversal BC

One set of congruent angles is {∠ABC, ∠BCH}

Another set is {∠ABK, ∠BCE, ∠BHC, ∠CBH, ∠GCH}

c.  Alternate interior angles

Alternate interior angles are a pair of angles on the inner sides of the parallel lines but on opposite sides of the transversal.

The sets of alternate interior angles are {∠ABC, ∠BCH}, {∠ ABC, ∠BCD} {∠BCE,  ∠CBH}, {∠CHJ, ∠GCH}

d. Corresponding angles

Corresponding angles are a pair of angles on the same side of parallel lines and on the same side of the transversal.

The diagram has no corresponding angles.

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24