Question

he circle shown below has AB and BC as its tangents: AB and BC are two tangents to a circle which intersect outside the circle at a point B. If the measure of arc AC is 160°, what is the measure of angle ABC? (1 point) 80° 40° 60° 20°

Answer 1

A quadrilateral has a sum of interior angles equal to 360.

Angle A & C are each 90 degrees, and we're given that AOC (arc AC) is 160 degrees.

Therefore
angle ABC=360-160-90-90=20 degrees

Answer 2

m∠ABC=20°

Explanation:

Consider quadrilateral ABCO. The sum of the measures of all interior angles in quadrilateral ABCO is equal to 360°.

Lines BA and BC are tangent to the circle, then the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,

• m∠BCO=90°;
• m∠BAO=90°.

The measure of the angle AOC is 160° (because the measure of arc AC is 160°). So,

m∠ABC+m∠BCO+m∠BAO+m∠AOC=360°,

m∠ABC=360°-(m∠BCO+m∠BAO+m∠AOC)=360°-(90°+90°+160°)=20°.