Question

IM NOT SURE IF THE ANSWER IS ACTUALLY C

Answer 1

D. 21

Explanation:

Given:

m arc AC = 69

Segment AB is tangent to circle O at point A.

We need to find the ∠ ABC

Solution:

Now we can say that;

By inscribed angle theorem which states that;

"Central angle is equal to arc subtended by it."

m∠O = 69 (Central angle)

Also Given:

Segment AB is tangent to circle O at point A.

Now by radius tangent property which states that;

"Radius which touches to closet point on the tangent is always perpendicular."

so we can say that;

m∠OAB = 90

Now in Δ OAB.

m∠O = 69

m∠OAB = 90

Now we know that;

"Sum of all angles of triangle is 180."

m∠O + m∠OAB + m∠ABO = 180

Substituting the values we get;

`69+90+m\angle ABO=180\\\\159+m\angle ABO=180`

Subtracting both side by 159 we get;

`159+m\angle ABO-159=180-159\\\\m\angle ABO=21`

Now we can say that;

m∠ABO = m∠ ABC = 21 (same angles)

Hence m∠ ABC is 21.