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:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.