The circle shown below has ab and bc as its tangents: if the measure of arc ac is 160, what is the measure of angle abc?

answer:

140

step-by-step explanation:

given that ab and bc are two tangents from point b

a and c are points of contact.

arc ac is 160 degrees means central angle subtended =320

and minor arc subtends 360-320 =40 degrees

consider the quadrilateral formed by the vertices a,b,c and o the centre of the circle

aoc = 40 degrees

at the point of contact tangents are perpendicular to radius hence other two angles are 90 each.

hence the 4th angle abc = 360-(90+90+40) =140

(since sum of angles of quadrilateral is 360)

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

the answer is 489

step-by-step explanation: