The figure below shows a triangle with vertices A and B on a circle and vertex C outside it. Side AC is tangent to the circle. Side BC is a secant intersecting the circle at point X: What is the measure of angle ACB? (6 points)
Select one:
a. 32°
b. 60°
c. 28°
d. 16°

A. 32°

Step-by-step explanation: how we find the measure of angle ACB is by taking the angle of arch BA and subtracting it by the angle of arch XA. then taking that number and dividing it by two.

so we know the angle of arch BA is 176° but we need to find arch XA. the angle of the arch XA is two times the measure of angle B

56 × 2 = 112

angle arch XA is 112°

now we plug both of those in for what i described earlier:

176 - 112 = 64

64 ÷ 2 = 32

angle ACB = 32°

hope this helped! :)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be