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:

the figure shows a circle with points a and b on it and point c outside it. side bc of triangle abc intersects the circle at po

what is the measure of angle acb? (6 points)

23°

32°

46°

16°

The correct option is C. 46°

Step-by-step explanation:

First find the measure of the arc AX

Now, Arc measure is twice the angle formed in the segment by the same arc

⇒ Measure AX = 2 × ∠ABX

⇒ Measure AX = 2 × 32°

⇒ Measure AX = 64°

Now we will use tangent-secant angle formula to find the measure of ∠ACB as ∠ACB is formed by tangent AC and secant BC outside our given circle.

⇒ ∠ACB = 0.5 × (Measure of major arc - Measure of minor arc)

⇒ ∠ACB = 0.5 × (156° - 64°)

⇒ ∠ACB = 0.5 × 92°

⇒ ACB = 46°

Therefore, The correct option is C. 46°

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for