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)

1 1/4 hours

step-by-step explanation:

2/4 + 2/4 + 1/4 = 5/4 or 1 1/4